I need to get rid of this trash!?

Okay, to make a long story short. I bought this storage unit and now I'm stuck with all this trash. I know, I was completely irresponsible to not have already considered the trash removal before I bought the unit. I'd put some of it in my own trash cans but my landlord doesn't pay for trash removal and just takes it away whenever he feels like it. Anyways, I was just going to take it to the dump, but because my car isn't registered to the town I currently live in I can't get a sticker to enter the dump. I don't want to just dump it in the woods either. So, how much trouble could I get into if I dump it in one of those apartment complexes dumpsters ?