How long can fish go without eating?

Your fish should be fine for that long large cichlids can go 2 weeks so depending on the size of your fish they should be ok.
 
Absolutely fine to leave them for that long...its not a fry tank though is it ?
 
I agree, i usually get someone ot feed them if I am going to gone more than 10 days, although most will tell you that they would be fine for up to 2 weeks.
 
If I'm gone more than a week I get a relative to drop in a few cubes of frozen food, every 2-3 days, and hide the flake and pellet foods.
 
AquariaCentral.com