Did the addendum on your lease include this notice of the 60 day requirement?
If so, then yes, you are liable for both the 60 day notice (but no greater than 60 days) plus the additional two months rent.
"What would it happen if I didn't tell them and just vacate the place?"
Then you can be sued for the remaining months of rent on your lease until the landlord can find a suitable replacement tenant for you.
Gail

