Recovering storage space on iOS 8.4 after having activated apple music

I updated my iOS device from 8.3 to 8.4 and then activated Apple Music.

It ate the free space that I had left on my device in a matter of hours.

It was frustrating as I permanently received the (running out of storage) message and no matter how many other apps I uninstalled, I could not determine where de hell the space was being sucked into.

I fiddled around and finally found the solution to my problem.