The cable your talking about is NOT the choke it is your idle speed adjuster, the choke is up on the left handlebar. if you were turning it like crazy your idle speed could be jacked way up or way down which could be a problem as well.

The choke cable runs on the right side of the F3's and ends in front of the carbs right under the bottom half of the airbox. it is just a simple pull cable that attaches to a bracket on the front of the carbs. Now since you broke the cable the carbs must be pulled to replace it so you can get the idle speed set correctly.