Closed loop PMDC motor control
I have used small Mabuchi motors that way and achieved results close to what you need using a velocity sensor which is crude compared to your slotted wheel. 

Start testing by controlling the motor with a PWM train that you can manually adjust up and down. Record the PWM duty cycle which gets you close to 6000 RPMs, this will be a starting power level. Then, bump the PWM power level up by one bit, and down by one bit, and record the resulting RPM change. Based on the values you record you should be able to predict how much power to add or remove from your center power level every 1/10th rotation when the velocity is too high or too low. 

At that speed it will be necessary to time the interval between slots with a hardware timer available on most microcontrollers. You won't be able to measure the velocity error of 1/10th rotation with sufficient precision using software. A 1 microsecond error in measurement will chew up your error budget.  

As alluded to in the comments, if you have a very dynamic load you may want  improve on the basic closed loop system to adapt to changing loads. In my project I found that the center power level was not the same for all motors. So I incorporated an integrating function such that if the sum of the errors over time was not 0 then I would adjust my center power level to try to bring the + and - errors closer into balance.