It’s a (very) low-end “DJ” mixer, so I am guessing there isn’t a balanced (XLR or 6.3mm jack) in sight. Which leaves RCA for output as well as for channel input.
But surely you don’t have to plug in the venue PA? Usually that is a (semi)permanent connection.
On the other hand, if they put in mixer like this, it’s a bit of a stretch to expect the rest is pro-quality and they have a serious sound engineer to set up things and maintain it.
The good news in that case is though … you can unplug the rca cable from the mixer output and stick it directly into your controllers output (just remember to stick it back after you’re done 🙂 ). In which case you can forget about their mixer. This obviously only works if nothing else is going on that depends on the mixer/PA while you are playing.
Cutting out the middle will, if not improve the sound at least prevent it from deteriorating the sound quality coming from you controller.
Greetinx.