...the left turn "rumble" sounds as if it could be a wheel bearing as that's when the o/s wheels are under more stress, the noise could still be there at all speeds and revs due to it being harder to hear through increased engine and road noise.
Next time you use the car check the wheels for excessive heat when you get home, most noises such as rumbling, squeaking, clicking, clonking etc etc are due to failed components resulting in metal to metal contact which generates heat. The wheels should feel slightly warm to the touch if everything is ok, if a wheel bearing is on its way out the wheel will feel a lot warmer or in a severe case too hot to touch.
If you find a wheel which is noticeably hotter than the rest jack up that corner and check for excessive play in the 6 o'clock 12 o'clock position. Good luck and hope you trace the problem.
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