What are wavelengths of RGB diodes?
By varying the intensity of either the red, green, or blue; it's possible to bring about any possible color that exists.


That's not quite true.



Figure 1. The CIE colour space and the colour space available with RGB sources marked at the vertices of the triangle.


If we had green and red light sources as shown above then we could vary the relative intensity of each to simulate any wavelength (colour) along the line from green to red. We are not generating the colour in question - it's just that the eye perceives it as such.
If we now add in a blue light source we can generate any colour within the triangle but not outside it.



  My question is, what are the wavelengths of the light that these blue, green and red LEDs emit? Does it depend on TV to TV or is it general?


It will vary. If you look at an LED datasheet you will see, for example, that the manufacturer offers "binned" LEDs. These LEDs have been graded after manufacture for light intensity and colour tolerance. A better display will have well matched LEDs and, for maximum range of colours, will have the R, G and B points as far apart in the colour space as they can for the target price.