im planning a manual conversion, i got a 99 Th sports for parts that is a 3.5 manual and i wanna put its gear box and other related crap in to my 3l te, are the gears boxes the same regardless of engine capacity?

i just put lows in the rear and king low in the front and when i hit a decent bump it feels kinda like the car is turning it self a little, surely this isnt ment to be?

3.5L box will work no worry's its just a longer 1st gear.