You need to configure fstab to set the proper permissions.

There is a whole page about how to do this on the Plex site, see: https://support.plex.tv/hc/en-us/articles/200288606-Mounting-NTFS-Drives-on-Linux

To make it short:

• Find the UUID of your drive:

  sudo blkid | grep ntfs

• create a directory where you will mount the drive:

  sudo mkdir /media/ext_NTFS_USB_Drive

• edit file /etc/fstab with command:

  gksu gedit /etc/fstab

• add a line to this file and save.

  UUID=485CBF485CBF3014 /media/ext_NTFS_USB_Drive ntfs-3g permissions,auto 0 0

  where the UUID is the one your drive and the mount point is the folder you created.
• now mount the drive:

  sudo mount /media/ext_NTFS_USB_Drive(you might get an error saying the drive is already mounted, in Nautilus for example. Just unmount it – Safely Remove Drive, or click the Eject Icon in Nautilus)

Now in Plex, you need to change the location of the media folder you were trying to add to somewhere inside: /media/ext_NTFS_USB_Drive