We propose and demonstrate hybrid white light emitting diodes enhanced with resonant nonradiative energy transfer in CdSe/ZnS core/shell nanocrystal solids integrated on near-UV InGaN/GaN LEDs. We observe a relative quantum efficiency enhancement of 13.2 percent for the acceptor nanocrystals in the energy gradient mixed assembly, compared to the monodisperse phase. This enhancement is attributed to the ability to recycle trapped excitons into nanocrystals using nonradiative energy transfer. We present the time-resolved photoluminescence of these nanocrystal solids to reveal the kinetics of their energy transfer and their steady-state photoluminescence to exhibit the resulting quantum efficiency enhancement.