Error authenticating for private-example-channel (LUMEN 5.8 with Redis)

I am trying to broadcast a channel for my client application from the lumen app using the laravel echo server. here I can successfully broadcast a public channel but when I try to broadcast a private channel my laravel echo server throw en error

Error authenticating qEWAcyHQxWrbCvFmAAAA for private-example-channel Error: Invalid URI "http:localhost:85/broadcasting/auth" I have checked my steps and found now the issue logically but here is something which I am might be missing.

what I'm doing for now is I have registered the broadcast service in the bootstarp/app.php file create event and provider and call that event from controller then init laravel echo server from lumen app and laravel echo + socket.io client for the client-side app.

// laravel-echo-server.json

{
    "authHost": "http:localhost:85",
    "authEndpoint": "/broadcasting/auth",
    "clients": [],
    "database": "redis",
    "databaseConfig": {
        "redis": {},
        "sqlite": {
            "databasePath": "/database/laravel-echo-server.sqlite"
        }
    },
    "devMode": true,
    "host": "localhost",
    "port": "6001",
    "protocol": "http",
    "socketio": {},
    "secureOptions": 67108864,
    "sslCertPath": "",
    "sslKeyPath": "",
    "sslCertChainPath": "",
    "sslPassphrase": "",
    "subscribers": {
        "http": true,
        "redis": true
    },
    "apiOriginAllow": {
        "allowCors": false,
        "allowOrigin": "",
        "allowMethods": "",
        "allowHeaders": ""
    }
}

//client side

window.Echo = new Echo({
  broadcaster: 'socket.io',
  host: window.location.hostname + ':6001',
  auth: {
    headers: {
      Authorization: `Bearer ${token}`
    }
  }
})
// window.Echo.channel('example-channel')
window.Echo.private('example-channel')
  .listen('NewMessageEvent', (e) => {
    console.log('hello', e)
  }).error(err => console.log('error', err))

//bootstrap/app.php

$app->register(Illuminate\Broadcasting\BroadcastServiceProvider::class);
$app->register(Illuminate\Redis\RedisServiceProvider::class);
$app->register(App\Providers\EventServiceProvider::class); 

// web.php

$router->group(['middleware' => ['jwt.auth'], 'prefix' => 'api'], function () use ($router) {    
Broadcast::channel('example-channel', function () {
        Log('chennal called');
        return true;
    });
});

//NewMessageEvent

<?php

namespace App\Events;
use Illuminate\Broadcasting\Channel;
use Illuminate\Broadcasting\InteractsWithSockets;
use Illuminate\Broadcasting\PresenceChannel;
use Illuminate\Broadcasting\PrivateChannel;
use Illuminate\Contracts\Broadcasting\ShouldBroadcast;
use Illuminate\Queue\SerializesModels;
class NewMessageEvent extends Event implements ShouldBroadcast
{
    public $message;
    /**
    * Create a new event instance.
    *
    * @return void
    */
    public function __construct($message)
    {
        //
        $this->message = $message;
        // $this->channel = $channel;
    }

    public function broadcastOn()
    {
        // return new Channel('example-channel');
        return new PrivateChannel('example-channel');
    }

    public function broadcastWith()
    {
        $data = $this->message;

        return ["data" => $data];
    }
}

//class NewMessageListener

  <?PHP

    namespace App\Listeners;

    use App\Events\NewMessageEvent;
    use Illuminate\Contracts\Queue\ShouldQueue;
    use Illuminate\Queue\InteractsWithQueue;

   class NewMessageListener
   {
    /**
     * Create the event listener.
     *
     * @return void
     */
    public function __construct()
    {
        //
    }

    /**
     * Handle the event.
     *
     * @param  NewMessageEvent  $event
     * @return void
     */
    public function handle(NewMessageEvent $event)
    {
        //
    }
 }

//trigger event

   event(new \App\Events\NewMessageEvent('this is the message from the event catch it if you can'));