Can cataract surgery improve my high myopia?

First, I assume by "high index" you mean you are very nearsighted (myopic), with a prescription of -11.00 in one eye and -9.00 in the other eye. By replacing your natural lens with an artificial one (an intraocular lens or IOL) during cataract surgery, your prescription can be changed however you wish.

Some “high myopes”—or those who are very nearsighted--choose to stay nearsighted, but less so. For example, changing your prescription from -11.00 to -3.00. This means you would still need glasses and/or contact lenses to see at a distance but would not have to hold objects so close to your face to be in focus for reading.  Others choose to end up with good distance vision without glasses or contact lenses, but may then need reading glasses to see up close.

Either way, the quality of your vision should be better as the cloudy lens (cataract) will be replaced with a clear one. Your personal "refractive target" is an important decision that you should discuss with your cataract surgeon before having surgery.