Cleaning toilet refill valve

My toilet has become very slow with water refill, so I was thinking it is probably necessary to clean the refill valve. However I'm struggling to actually open the mechanism and get to the valve. See in the attachment a picture of the mechanism - I've been trying to open the plastic lock nut, but it's is not moving at all. Do you have any ideas on how to open it? Or maybe I'm doing it all wrong? All help will be appreciated! Thanks! Attachment 50099 (http://www.doityourself.com/forum/attachments/toilets-sinks-showers-dishwashers-tubs-garbage-disposals/50099-cleaning-toilet-refill-valve-compact-2099b.jpg)