The plasmonic Dicke effect means a cooperative emission mechanism of multiple light emitters when they are simultaneously coupled with the same surface plasmon (SP) mode of a metal nanostructure to achieve a higher collective emission efficiency. Here, we compare the enhancements of emission efficiency among a series of SP-coupled InGaN/GaN quantum-well (QW) structures of different QW period numbers to show an emission behavior consistent with the plasmonic Dicke effect. The relative enhancement of overall emission efficiency increases with QW period number until it reaches a critical value, beyond which the enhancement starts to decrease. This critical QW period number corresponds to the effective depth range of the plasmonic Dicke effect in a multiple-QW system. It also represents an optimized QW structure for maximizing the SP coupling effect. Internal quantum efficiency and time-resolved photoluminescence are measured for comparing the enhanced emission efficiencies of blue and green QW structures with different QW period numbers through SP coupling induced by surface Ag nanoparticles.