Graphene-based organic light-emitting diodes (OLEDs) have recently emerged as a key element essential in next-generation displays and lighting, mainly due to their promise for highly flexible light sources. However, their efficiency has been, at best, similar to that of conventional, indium tin oxide-based counterparts. We here propose an ideal electrode structure based on a synergetic interplay of high-index TiO2 layers and low-index hole-injection layers sandwiching graphene electrodes, which results in an ideal situation where enhancement by cavity resonance is maximized yet loss to surface plasmon polariton is mitigated. The proposed approach leads to OLEDs exhibiting ultrahigh external quantum efficiency of 40.8 and 62.1% (64.7 and 103% with a half-ball lens) for single-and multi-junction devices, respectively. The OLEDs made on plastics with those electrodes are repeatedly bendable at a radius of 2.3 mm, partly due to the TiO2 layers withstanding flexural strain up to 4% via crack-deflection toughening.