Horrible plumbing in my rental apartment?

I just moved from NYC to Southern California. I have always had cats and have lived with my boyfriend/now husband for the better part of 10 years. We have never had plumbing problems before, but ever since moving in to this apartment 5 months ago, we've had nothing but plumbing problems. For a while it was just a slow drain on one toilet. The landlord would snake and it would be fine for a while and then it would get slow again. Then last month, one morning out of nowhere, both toilets and both showers started spewing sewage in unison at 7am! A real plumber came, snaked from the basement/garage and told me to stop flushing litter. Done. Now it seems the toilets are starting to drain slowly again. Can I use rid-ex even if we don't have a septic tank? Any other suggestions to keep things flowing? Thanks! I am adding details to answer some of the questions/suggestions raised in the answers: 1 - THANK YOU to those of you responding 2 - I don't want to move, everything about this apartment is perfect except for the plumbing. 3 - The landlord has assured me it is not a problem with the roof vent, though I don't know how he knows this. 4 - None of the plumbers could identify what they snaked but one suggested we stop flushing our flush-able litter. 5 - I just want to know what I can do to help the plumbing running smoothly. I know it's not technically my responsibility, but it would certainly make my life either. 6 - Is Ridex safe for non-septic systems? THANKS!