user unable to write to media | Permission denied

I am having a problem utilizing a mounted drive on my Raspberry Pi 2B running Diet Pi.

dietpi@DietPi:/media/dietpi/Other$ sudo chmod 666 -R /media/dietpi
dietpi@DietPi:/media/dietpi/Other$ touch text.txt
touch: cannot touch 'text.txt': Permission denied
dietpi@DietPi:/media/dietpi/Other$

The media appears to be mounted correctly as I am able to read what is in the drive. **Other Steps Attempted**

sudo chown -R dietpi /media/dietpi

This returns numerous of the following error:

chown: changing owndership '/media/dietpi/: Operation not permitted