The RCA cables are usually stereo (i.e. red for right/white for left). If you use PA speakers like you have, you’d have to split a regular cable in order to go to both left and right speaker.
If you are using something like this now: http://www.simplifiaudio.com/speakers/images/dsp_rca2xlr.jpg you have the wrong cable.
If you are using one of these: http://www.avacab-online.com/WebRoot/StoreES/Shops/63690703/51CA/CDE6/E611/D8EF/A34B/C0A8/29B9/37EF/CORDIAL-CFU-MC-Avacab.jpg you had to split this into two separate “mono” cables.
That would make it look something like this: https://images.monoprice.com/productlargeimages/47771.jpg
Never mind the male/female end in this pics (you need male to go into speakers) or gold connector (waste of money for PA). Just to show you the options.
That said, you are right that going more than a few metres/yard, you should be using balanced cables.
Good thing is there are some options for you:
1) Unbalanced to balanced converter: http://artproaudio.com/isolators/product/cleanbox_pro/ This will not only give you balanced XLR outputs (they have a DTI box that does that too), but also changes the levels. RCA output levels are different than balanced output levels. These boxes fix that for you. They cost about 80 euro here.
2) Get a small PA mixer. I am a big fan of the Yamaha AG and MG series. Go for the 6 channel options in your situation. You plug in your unbalanced controller, have an option for a backup music source, (more) microphones with some EQ/FX options, an option to also plug in a guitar (if you have a sing-a-song writer performing for example).
The AG series has a built-in soundcard, so let’s you record or play stuff direct from a laptop too. AG06: https://www.yamahamusiclondon.com/sites/ymlv5.90/productimages/big/CAG06_e.jpg
Pricing is about 130 euro. So 50 euro more gets you all the extra features. It would be my choice (I actually have an AG03 on my desktop hooked up to my computer and monitor speakers).
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