In order to be able to use the hotkeys and to change the backlight brightness at all, it takes some further steps after installing Ubuntu / Linux Mint / any other compatible linux distribution.
First you need to install nvidia-current from the repository (for me, it installed nvidia-graphics-drivers-304).
sudo apt-get update sudo apt-get install nvidia-current
I rebooted my machine after installation to enable the driver. This might not be necessary and could also be done when all steps are completed.
Next we need to create a new xorg.conf file. Nvidia gives us a tool for this:
sudo nvidia-xconfig
This will create a new config file in /etc/X11/. Now open the new config (/etc/X11/xorg.conf) file with your favourite text editor.
Before:
Section "Device"
Identifier "Device0"
Driver "nvidia"
VendorName "NVIDIA Corporation"
EndSection
After:
Section "Device"
Identifier "Device0"
Driver "nvidia"
VendorName "NVIDIA Corporation"
Option "RegistryDwords" "EnableBrightnessControl=1"
EndSection
Add the additional line and save the config file.
After these steps you need to reboot your machine. If you already did this after installing the drivers, it should be enough to restart X.
Sources: