Welcome to the forum. They should both have the same transmission. Are these the S series or the regular ones? Seems like there's a bolt on the top of the tranny you can pull to add fluid. It's the one with a copper crush washer on the lower, left hand side of the top plate (as you're sitting in the seat and staring down at it).
The 7610 I had had the rear fill tube like the 5610, but it did have those nice foot rests that I ordered and put on my 5610.