Cannot access /media/username folder - permission denied

Question

I have installed Ubuntu 18.04 recently and while installing I have created a separate partition /media/username in order to be able to share files with potential future installation as advised here. However, it seems I cannot access this partition - I can't see it in Files explorer and when I attempted to create and save a file there through a command line I obtain Directory is not writable notice. The same goes with trying to move a folder to /media/username - mv: cannot create directory './my_folder': Permission denied. Moreover, I plug in the external disk and I can see it displayed within the same folder. What may be the reason of all of that?