Some of the things I would try:
pipe wrench....see if it will go in the tightning direction too;
sometimes there is a bit more play by doing this proceedure and it will
break the bond of whatever is binding. Work the nut a little at a time
in both directions.
some kind of lubricant such as WD40 (let it sit awhile so it migrates)
CLR wash for mineral deposits
Gently heating with hair dryer
Gently tapping the nut (not only helps with bond breaking but also
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