Power and RCA do sometimes interfere with each other, its always best practice to run them down seperate sides.
However i;ve done plenty of installs for people where cables have all gone down the same side and theres been no interference - depends on equipment and installation.
Best bet is to check that the grounds are nice and solid, make sure the surface you are grounding to is good and clean - no rust, corrosion or paint on there and then tighten the wires up. If you have a multimeter i would also check the grounding to ensure that the resistance is low from amp to ground.
You can buy suppression kits that are supposed to elimate the noise, i've always found these totally useless, at best cutting the noise down but not eliminating it.