I don't think the CPU is limiting. How much RAM do you have in it? Is the game installed on the SSD?
What kind of monitor do you have? and what kind of temperatures do you have in the whole system?

Since the games I am currently playing (CS:GO) are very CPU heavy. When changing graphics settings from medium to high, for example, there is no difference in FPS because the graphics card (NVIDIA GTX 1080) is more than sufficient. However, you could get a lot more out of the game with a better processor.

What makes you think your 6700 is a bottlneck?