Headphone Impedance

Not sure which forum to post this question.....

I understand that getting an external headphone amp / headphone combo would be the best way to go but I'm looking at using headphones late at night for background listening while doing some reading.

Therefore, I would be looking at using the headphones with the built-in headphone amp / connection on the new Linn Akurate Kontrol.

If I use the Linn Majik-I integrated pre-amp as an example, the user manual states the following information:

Output impedance:
Line out -> 300 Ω
Tape out -> 300 Ω
Headphones -> 11 Ω

So does this mean that this pre-amp will work best with low impedance headphones like the Grado headphones (32 ohms)?

What happens if I use higher impedance headphones like the ones offered by Sennheiser or Beyerdynamics? Does it mean that I would need to raise the volume?

Also, does impedance value affect sound quality?