Error in code based off negative numbers. Need possible fix on time calculator. Need help on where i should add the additional minutes of the day

Hi I have created a program in C++, (which I am very new too). This program basically asks the used for two times such as 3:57 and the duration 1:05 and it will tell you the sum and the difference between the two. The problem is I am getting negative remainders such as if I put an input of 1:18 and 10:39 I expect 11:57 and 2:39 but I get 11:57 and -9:-21 as result when I run the program. What should I do? This is for an assignment and we cannot use if statements. The instructions say if we are having this problem we should " This is easily done by adding a day (or two or three) to before when calculating the difference." I do not know what this means and have been struggling on this. i pass most tests besides when the time goes negative code is below:

#include <iostream>
#include <string>
#include <iomanip>
using namespace std;

int run()
{




    cout << "Give me a time (such as 3:57) and a duration" << endl;
    cout << "(such  1:05), and  will tell you the sum" << endl;
    cout << "(that is the time that follows the given time" << endl;
    cout << "by the given duration), and difference (the time that proceeds the given time by that duration)."  << endl;

    cout << "Time: " << endl;
    int timeHours;
    int timeMinutes;
    char discard;

    cin >>  timeHours >> discard >> timeMinutes;


    cout <<"Duration: " << endl;
    int durationHours;
    int durationMinutes;

    cin >> durationHours >> discard >> durationMinutes;



int time = timeHours * 60 + timeMinutes;
 int duration = durationHours * 60 + durationMinutes;
 int after = time + duration;
 int before = time - duration ;
 int afterHours = after / 60 % 12  ;
 int afterMinutes = after % 60;
 int beforeHours = before  / 60 ;
 int beforeMinutes = before % 60;



cout << endl;
 cout << durationHours <<":" << durationMinutes << " hours after and before, "
 << timeHours << ":"  <<timeMinutes << " is ["  << afterHours   << ":" << setw(2) << 
setfill('0')<< afterMinutes <<", "
 << beforeHours << ":" << beforeMinutes << "]" << endl;
return(0);
}

Any help to make this program work properly is greatly appreciated. I am new to C++ and very frustrated.