Check which group you and plex belong to:

groups
groups plex

Now, add plex user to your user group, and allow this group to access /media/$USER:

MYGROUP="$USER"
sudo usermod -a -G $MYGROUP plex
sudo chown $USER:$MYGROUP /media/$USER
sudo chmod 750 /media/$USER
sudo setfacl -m g:$MYGROUP:rwx /media/$USER
sudo service plexmediaserver restart