Output load of led strip dimmers
The RGB controller's output is only relevant to the 3-color LED section.   Per 60 LEDs, they use 0.4A per channel (1.2A total).  48 watts is 4 amps.  

So if your strip is less than 10 feet long you should be within limit of that controller. 

If you are near or exceed the limits of that controller, you can add a device called an amplifier in between the controller and the LEDs. The same controller can power several amplifiers if needed. At that point, the controller's output is no longer used for power, but merely as a signal to the amplifiers.  So if the signal has some distance to go, it can travel on thin thermostat cable instead of heavy cable. 

You will not be able to use the RGB controller to dim the monochrome strips.   It will not do what a person expects, unless they know a lot about RGB blending, which your guests won't.

Also keep in mind these cheapie LED dimmers are not intended for use as on/off switches, and will leave components energized even in the "full off" position.  Not something you want to do.  Aside from being a fire risk, it will be a considerable vampire load 24x7, which will drive up your energy costs. 

The better way to think of dimming is as a fine adjustment after the switch.