I have absolutely no idea what you mean by "different internal forces". Perhaps it would help if you told us what you mean by "end 1" and "end 2".
I might guess that you mean you have two boxes, of masses m1[/sup] and m2 abutting and by "pushed on end 1 and end 2" you mean on the one hand pushing on box of mass m1 so that both move or on the other pushing on the box of mass m2 so that they both move.
The obvious points are: Either way, since you are accelerating the same mass, m1+ m2, in the same way, you must apply the same force. However, is m1 < m2, the force that box m2 must apply to it, it you are pushing on box m2, is less than the force box m1 must apply to box m2 if you are pushing on box m1.