How do wavelengths add-up?

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.

Wavelengths are one to one only with the spectral colors, and wavelengths do not add up to a new one, they remain distinct .

It is the perception of color which is a biological function, due to the receptors of the eye, which creates new hews and colors when more than one wavelength falls on the retina of the eye.

The perceived color will depend on the combination of wavelengths according to the plot above.