No AAA.
My commute is 11 miles each way. I carry a spare tube, pump, patch kit, multi-tool (spoke wrench/allen keys/screwdrivers), and some zip ties. Total cost was probably 40$. I've patched a couple tires, trued a wheel well enough to get home after breaking a spoke, adjusted my seat/handlebars/derailleur on the road easily. Even helped several cyclists who I came upon on the side of the road in need of assistance. It takes about 10 minutes tops to change a tube and check the tire for debris, less time for the other things.
With my kit you would be on your way long before AAA ever showed up, for less money.