How add to github CI access to private repository?

in my pubspec.yaml i have

  private_repository:
    git:
      url: git@github.com:owner/private_repository.git
      ref: main

what i need to add to github CI is work ?

 steps:
      - name: Checkout source code
        uses: actions/checkout@v2
      - name: Install Flutter
        uses: subosito/flutter-action@v1
        with:
          channel: 'stable'
      - name: ssh
        uses: webfactory/ssh-agent@v0.5.4
        with:
          ssh-private-key: ${{ secrets.SSH_PRIVATE_KEY }}
      - name: Get packages in a Flutter project
        run: flutter pub get

i generate ssh : ssh-keygen -t rsa -b 4096 -C git@github.com:owner/private_repository.git -f gh-pages -N ""

and add to secret repository

when I start pub get I don't have access to the repository

i have to add the keys somewhere else ? should i add SSH keys in acount repository's owner ? (I am not the owner but have access)