Speed Current Relationship in İnduction Motors
You miss something.

The synchronous speed depends on frequency, this is the 'zero torque output' speed. An induction motor typically runs at a little below synchronous speed. 

The amount it runs slow is called the 'slip'. 

For small values of slip, the current it draws is proportional to the slip, and to the voltage. This means the torque, which depends on current, is proportional to slip at constant voltage.

If a motor was running at some small value of slip (say 3%), and you increased the voltage while keeping the load on the motor constant, then the slip would reduce a little, perhaps to 2.5%. This means the speed would increase, but not by much. If the synchronous speed was (say) 1800rpm, it would increase from 1746 rpm to 1755 rpm.