How do I wash the "pokey" side of a box grater? I have this box grater, and one of the sides is "non-directional" (not sure what this is called) -- that is, the pointy "blade" things are on every side of the holes:



Close-up:



The fibers you see are from ginger.

My question is: How do I clean this side of the grater?


Sponges and rags get torn apart and the fibers are left on the grater.
Brillo pads same deal, of course.
I tried rubbing it out with my fingers but, you know: Ouch.
Even scrubbing from the inside doesn't do much like it does for the directional sides of the grater. The food isn't stuck in the holes, it's stuck on the little points.
Rinsing it under the highest pressure water my sink has doesn't blow away the food matter either, it's just all snagged there pretty tightly.
I found this page about graters and the author there seems to just avoid that side of the grater specifically because of how hard it is to clean, so perhaps there is no hope here.
I do not have a dishwasher. 


Even though the above picture has ginger fibers on it, I'm not looking for techniques just for this specific case (that just happened to be what was stuck on the grater when I took the picture). I have the same problem with this side of the grater no matter what I grate, e.g. cheese, even hard cheese, leaves bits of cheese there, which are slightly easier to remove with hot water than tangled fibers are, but still not easy.

What can I use to quickly and conveniently clean this after each use? The cleaning difficulty makes this my least favorite kitchen tool. I'm never excited when it looks like I have to use it.
A dishwasher gets cheese off even that side - but that's no good if you don't have one, nor is it very effective against ginger and other fibrous foods. 

The best I've found is simply a washing up brush (i.e. plastic bristles and a long handle) from both sides. I would then put it in the dishwasher for a final clean unless I'm doing a proper load of washing up, which is rare