You stated that the Hummm occurs on "sweeping" left hand turns. Does it do it while sitting still and turning to the left? If not, then it might not be a problem with the hydraulic system. Have you checked for a bad wheel bearing ? There is generally a lot more pressure exerted on a wheel bearing when making a turn than in traveling in a straight line. And , usually, the bearings opposite the direction of the turn will be the culprit , just like the nasty clicking noise of a bad CV joint on a front wheel drive car, when it clicks turning left, it is usually a bad joint on the right causing it. I am no expert in car repairs, since I have worked at a Mack truck dealership for many years, but, cars are just little trucks, lol..

 

Different bushings and seals to each side?

 

I think you Caddy is humming because it's just happy to be alive.

 

good point .. is it the Cadillac song?

 

Noise in one direction and not other : steering gear likely cause. also check for grounded P/S hose.