White light does not have a single wavelength but instead is described by a spectral distribution, which is not uniquely determined. There are many light compositions that can pass as white. The spectrum of the white light from the three LEDs combined is just the sum of the individual LED spectra, weighed with the proper intensity. Likely, your LEDs are also only approximately described by a single wavelength. Other white light may have a different spectral composition but will still look white.
Your eyes sense just 3 colours, red, green and blue. Note that the sensitivity of the cone cells in your retina also has a spectral width about the central color.