There are a number of factors that need to be considered for your highly near-sighted prescription.
1. Corneal thickness - laser vision corrections on the cornea reduce the thickness of the cornea in order to flatten it. If your prescription is too high or the cornea is too thin, it is not safe to perform a laser vision correction.
2. Initial corneal curvature - Since the cornea is being flattened, if your cornea starts off relatively flat and must be flattened further, the result could cause problems with aberrations or dryness.
3. Pupil size - A larger than normal pupil size would exacerbate vision problems as it could require a larger optical zone for treatment.
4. Prescription history - If your prescription has been increasing steadily over time than laser vision correction might be unsatisfactory as the prescription could continue to change.
5. Eye health - The eye must certainly be checked for other possible problems prior to surgery such as keratoconus or retinal tears or detachments.
Often a surgeon will recommend a phakic intraocular lens for this high prescription but there are certainly many people who have had laser vision correction with a -11 Rx and are very happy. You just need to realize the risks and find a surgeon that you feel confident could perform the correct procedure (or no procedure if it turns out you are not a good candidate).