I found tons of topics about sound issues, some of which pointed me in the right direction to find the cause of the problem, but I failed to find a solution.
Sound works out-of-the-box on LMDE on my machine.
I can control the volume using sliders in the mixer.
I can also push multimedia keys on my keyboard, which causes a nice animation of volume getting up or down in the middle of the screen.
But pushing the multimedia keys does not really change the volume. After some investigation I realised, that multimedia keys change the volume of another mixer (ALSA I believe).
Does anyone know a solution to this? I do not care if the solution makes me use pulseaudio or alsa. It would be best to use the one, which is considered default for LMDE. I am so confused, I don't even know which one that is.