I would take a sharp knife (not serrated) that you don't care if it gets dulledor nicked, and heat it up with a lighter or candle and when it starts getting a little red, quickly press it onto the side of the nylon nut. A couple tries of this will melt/cut right through it and you can stick a screwdriver into your cut and twist to liberate the nut. Be sure to be gentle and resist prying against the porcelin (sp) so that you don't crack your toilet. I'm sure others will have other ideas too...