dedicated electrical line

Both . It is called an 'isolated ground'.
Quite often found on sensitive equipment in hospitals and computer rooms .
WARNING , not every electrician knows how to install an isolated ground correctly !
While dedicated lines and isolated grounds will give you maximum performance , they are only needed if you are having problems that will be alleviated by their use . Can you hear noise on your system when appliances cycle on and off such as your HVAC , refridgerator , microwave , small kitchen appliances or flourecent lights ?
Can you unplug items that are on the same circuit as your audio equipment during listening sessions ?

If you do need to run dedicated lines , do at least two 20 amp circuits , one for your analog equipment and one for digital .

Good luck .

I read that grounding rods are supposed to be at least 6ft. apart .

When I read up on power conditioners , I found that they impart their signature or had a sound . Just the same as anything else in the system chain .

I am assuming that you do have some interference problems , or noise , coming from your speakers . Can you identify the culprit ? Is it possible to eliminate the problem during listening sessions by unplugging or turning off the power ? Just a thought .

Good luck .