Without knowing the exact conditions of your contract, it's not that easy to help you.
In case that you really have the right to cancel the contract every time within a 1 month notice, it should be no problem to end the contract at that date - but this is very unusual.
Usually contracts have either a run time of one or two years initially and extend for another year if not cancelled at the right time (one or three months before the contractual term ends - one month only for contracts with an inital runtime of one year, three months for two-year-contracts).
If you cannot cancel your contract at that time, you might be able to cancel it prematurely due to leaving Germany. But therefor you'll also have to proove movement with legal statements ("Abmeldebescheinigung") -and- you'll have to pay for 3 months AFTER leaving Germany. So it really depends on your contract...
