I haven't gotten to Mithran Fishing Rods yet, BUT I have a fail-proof method to break normal fishing rods.
Get a few stacks of Meatballs and go to one of the deep pools in Gusgen Mines ((F-G-6), (H-6), (I-6) on Map 3)--the pools where the NM ghosts with silly alliterative names are. Gavial Fish is the only type of fish in that pool and it can only be caught with a really strong pole (Composite, Ebisu, Lu Shang) and with that bait, so whenever you see the 3
really negative messages:
"You are positive you don't have enough skill to reel this one in."
"You have a bad feeling about this one."
"You have a terrible feeling about this one."
then it's definitely a Gavial Fish and you can successfully pull it up like a regular fish, and--voila!--broken rod.
(And then if you try to fish again you get that silly little message that says, "You can't do that without a rod in your hands," and if you're a guy that's NOT THE
ONLY THING--shutting up. :x)
G'luck ^^/
-edit- Oh, and you
don't need fishing skill. I actually skilled up 0-3 this way, lol.