The unique properties of surface plasmons (SPs) are expected to provide a great improvement of light extraction in light-emitting diodes (LEDs). Surface plasmon modes are characterized by a high local density of states, and if scattered by gratings, significantly high emission enhancement is achievable. We investigate the physical role of SPs in improving light extraction from GaN quantum-well (QW) light-emitting structures incorporating metallic grating, by using first-principle theory based on Maxwell's equations and fluctuational electrodynamics. We demonstrate how careful nano-engineering, specifically by choosing the right nano-grating period, can reduce absorption losses and provide optimal enhancement; in the investigated test geometries, light extraction is increased by a factor of four, with the plasmonic losses being reduced from ~ 90% to below ~ 60% thanks to the metallic grating. While the results confirm a strong enhancement and reduction in the plasmonic losses, the overall losses still represent a significant obstacle for plasmonic-enhanced emission. With further optimization of the structure, the grating shapes and the materials, a much larger enhancement and lower losses are expected to be possible.