Unfortunately, your question is actually harder than that.
First, what do you mean by "white"? There are different color temperatures in use, from somewhere around 1800K to around 10000K. "white" will be a lot more yellow/red at 1800K than at 10000K (or, the more "normal daylight" around 5000K.)
Deciding on what "flavor" of white you want is step 1.
Second, each diode has a different PWM-to-output function. This has to do both with the actual voltage/power efficiency of each emitting diode, and also possibly with differences in gamma response of each of the diodes. You will need to look up the specifics of these values in the data sheet for your specific device -- and even so, cheap LEDs may have significant variation (like, +/- 20%!)
Third, the diodes may not match exactly with the center frequencies of sensitivity of the eye color receptors. If so, then output power in one of the LEDs may actually trigger some mix of perceived input in the eye. You have to compensate for this in your math.
All in all, this means you can construct a non-linear (because of gamma and LED response curves) and non-orthogonal (because of non-matching center frequencies) system of equations, where you put in the temperature of white that you want, and out comes the relative PWM ratios of your particular RGB LED.
If you're not interested in actually getting it right mathematically, the simplest thing to do is to shine a "known white" reference lamp onto a white piece of paper, and shine your LED right next to it, and adjust the three gains until three different human beings agree that the two spots of light have the same color. One step up from that is using a calibrated color meter; perhaps you can use one of those used to calibrate computer monitors if you want something cheap.