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 .

Hi, An isolated ground would require a separate grounding rod(s). What you need to do is disconnect the ground currently going to your receptacle, and simply run a 8 GA or 6 GA from your newly installed grounding rod(s) to the ground on the receptacle.

Would you ever be concerned about the distance between grounding rods? That you might possibly create a "battery effect", or difference in potential between grounds?

Dedicated lines are the way to go. Also, put the breakers on the opposite phase of the fridge, install at the top of the rail if possible and clean the new breakers before they are put in. This is well worth the trouble and expense.

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