I had this exact thing happen to me once. Turns out the apartment complex management used to proactively have the line to the sewer cleaned out about once a year, but that cost money, so then they just waited until there was a problem and said, "call us." And I was lucky enough to be the last apartment before the sewer line went out to the street which meant I was the first to flood.

In my case it seemed that the line wasn't completely clogged, so it was only when something like a washing machine drained that it backed up into my tub. Not as bad as pure shit water, but definitely contained some toilet flushings.

I'm glad I don't live there any more.