this easy method has worked wonders on
some ugly coins and turned them into real nice coins:
soak in tap water with heavy dose of counter top
dish soap - check every few hours, brush lightly with a softer toothbrush that hasn't been chopped down ...and then leave in the solution overnight..or several days...checking regularly and doing the light brushing each time... maybe refreshing the solution every day...until desired results are achieved
next time I get a 'new' one I will post before and after pics. I don't have any dirty ones at the time being
and if you are going to try this, do it on a junkier coin first and see how it goes..or several that you haven't been able to get clean
works best on claudius ii or gallienus or similar era...