It all depends on whether the pulled appliance has a regular flat, steel tongue, with a hole in it, to accept a bolt or hitch pin. Yhe pulled appliance may have 2 flat steel plates, that would then slip over a single plate on the draw-bar of the tractor. This is the usual way of attaqchment.
Now, if your attachment has something else on it, that will only fit your tractor, well yes, you might have to buy the one made for your tractor.
But--I haven't seen anything that won't mate up to the standard drawbar on a tractor, be it Craftsman, or any other brand!

All pull behinds designed for tractors are all universal fit.

No, you don't need a Cadet-brand sweeper or cart. Generally, lawn tractors have a universal drawbar plate as described by Rusty. When you get into garden tractors, a few have 3-point hitches, which are similar to what you will find on farm tractors. Plus, a few attachments will require a sleeve hitch, which is purchased separately. Your Cadet lawn tractor is not intended for use with ground-engaging attachments, but will pull a cart, lawn sweeper, fertilizer spreader, or aerator, all of which have the standard hookup that Rusty described.