Who do I complain to about un-fixed repairs in my apt. that the landlord/maintenance is not takin care of?

I rented out a apartment back in December and I have called maintenance over 20 times about different issues with the apartment from toilets being backed up, to overflowing, sinks being clogged, garbage disposal leakage,etc. Now I have new neighbors upstairs and everytime they use there garbage disposal whatever they are disposing comes up in my sink! Maintenance came about a week ago and put something down the drain but that didnt do anything. Last night I contacted emergency maintenance and told him they needed to do something b/c now my sink is stopped up full of water and someone else dinner and I was told that wasn't consider an emergency and he would contact a plumber but no one never showed up. Would I be allowed to break my lease w/ no penalty in a situation like this? b/c Im getting sick and tired of dealing with issues w/ this apt.!