The point of a high cadence is NOT to go faster, but to ride at your current speed and power output, but using less force and more speed on the pedals. You dont expect to spin at the same gear you grind. This would take more power, and when you are riding your fastest, you dont have any more power.
You should start by training your legs to spin fast at a lower speed. When you can move your legs fast, you can then gear up a bit and ride with max power. At this point, you should be riding in a lower gear than you would currently choose.

Spinning may make a marginal improvement to your speed, a bigger improvement to your endurance, and a significant lengthening of your useful knee lifespan.