11 mph isn't bad if you are new and getting into shape. I just resumed riding last year after about 33 years off and used to get passed all the time. Now some people pass me and I pass some others.
Yes cadence is important, you need to find what's best for you, 90 is a reasonable starting point. Is your seat high enough? Sitting on the seat with your heel on the pedal at its lowest point, your leg should be completely straight - this is a starting point, adjust from there. Where do you place your feet on the pedals when riding? Ball of foot should be over the center of the pedal. Are your tires fully inflated? How much do you weigh? if you are near 200# or more run the rear tire at maximum pressure per the tire sidewall- front can be 10 less, try it there and adjust to your own preference. Is your bike well adjusted? Brakes not dragging? Shifts well? Wheels run true?
Shifting - shift so that you can comfortably maintain your cadence, especially don't overstress your knees by pushing too hard. You'll run a higher gear riding downwind than you will upwind. When I'm riding trails that pass under roads, if the trail is otherwise level I'll often not shift at all, or just up or down one gear, just depends how I feel, how fast I'm going, how crowded the trail is, etc. But when I was starting out I'd shift down to my front granny gear coming up the other side.
I also started doing some stretches and exercises for hamstrings, IT band, leg muscles, core and back. Don't expect overnight results but you should see steady progress. I went from gasping after 5 miles in September to riding a metric century in March and feeling tired, but good when I was done. It is a lot of things all cumulative. Again seat height is crucial.