Changing CI actually makes most difference at lower levels.
At CI 10, your cruise mach at FL370-390 is likely to be around .77. At CI 50, about .79. That's a change of less than 2 minutes per hour - for a three hour cruise, about 5 minutes better. Your climb speed might change from 270-300, and similarly descent speed, which at a guess would net you another 4-5 minutes.
However, the difference between cruise speeds at FL290/310 (as you may end up on an ATC restricted route) is likely to be significantly different. CI 10 at FL270 is painful - with anything like a tailwind, you may end up at an IAS of about 240 kts, which is just WRONG (but might unfortunately be company policy).