You'll need to read your lease, but usually in Texas if neither party gives 30 days notice, your lease changes to "month to month".

If you give your notice before the end of this month, you would be set to leave 30 days from now. You still have to pay for the time that you'll be in the apartment till then however, which means paying November's rent, minus any days you wouldn't be there. When you give your notice, your landlord can probably write up some paperwork and accept money for the prorated rent instead of the whole upcoming month.

I wouldn't suggest not paying your rent under any circumstances, as this pretty much kills any chance you have of bringing any kind of suit against your landlord for any issue.