Plumbing codes are different in each state but your 11' vent will be much b3etter than none at all. The only problem is, it sounds like you will be running this vent inside the cabinets, whereas a vent is not supposed to go horizontal until it is 6" above the flood rim of the highest fixture on that floor; and the vent should run in an uphill grade to provide for drainage of condensation in the pipe.
It may be possible to run the drain 3' or so to the side of the sink, then run the vent up through the roof and the drain down through the floor at that point. Of course, each penetration of the roof is another potential leak, so the vent could be run up to above the top plate then across to the main vent. The vent can be run up to 25' in this manner. This could be much more comfortable to run than draining through the cabinets.