Why can I not create a directory on my external hard-drive?

When I try to make a new directory on my external hard-drive I get a message saying that it is a "Read-only file system"

LU06296APPLE:~ fortinok$ mkdir /Volumes/Seagate\ Backup\ Plus\ Drive/working_files
mkdir: /Volumes/Seagate Backup Plus Drive/working_files: Read-only file system

However, it looks like from the permissions, that the owner of the drive should be able to "write"

drwxrwxrwt@  5 root      admin                    170 Feb 16 09:02 .
drwxr-xr-x  34 root      wheel                   1224 Feb 13 16:00 ..
lrwxr-xr-x   1 root      admin                      1 Feb  2 08:28 Macintosh HD -> /
drwxr-xr-x   1 fortinok  LONGWOOD\Domain Users   4096 Feb 15 22:34 Seagate Backup Plus Drive

Since I am the logged in user:

LU06296APPLE:~ fortinok$ who
fortinok console  Feb  2 08:58 
fortinok ttys000  Feb 13 07:55 

and I "own" the drive, why can I not make a new directory?

(Note: I am also unable to make a new directory using Finder.)