The version of the drivers should always match the version of the kernel. If you, for any reason, need v5.11 of the driver, you should install v5.11 of the kernel.
In addition, the numbers you are quoting look very strange. Please post the output of
$ uname -a
$ dpkg -l | grep ii | grep \ linux-
$ dpkg -l | grep rc | grep \ linux-
and the list of repos you have
$ grep ^ /etc/apt/sources.list /etc/apt/sources.list.d/*
-Why the software update doesn't make it?
Perhaps you didn't do
$ sudo apt-get update
Please post the exact command you used when trying the update.
-Is it ok to install it myself via the terminal?
What do you mean by this?
Using apt (this is ok), or installing from .deb (not recommended, but if you need it...)?
I never tried it with the type of installation you mean to do, but if you want to install from .deb I guess gdebi is also preferred instead of dpkg.
