The maximum peak power of ultrafast mode-locked lasers has been limited by cubic nonlinearity, which collapses the mode-locked pulses and consequently leads to noisy operation or satellite pulses. In this paper, we propose a concept to achieve mode-locked pulses with high peak power beyond the limitation of cubic nonlinearity with the help of dissipative resonance between quintic nonlinear phase shifts and anomalous group velocity dispersion. We first conducted a numerical study to investigate the existence of high peak power ultrafast dissipative solitons in a fiber cavity with anomalous group velocity dispersion (U-DSAD) and found four unique characteristics. We then built long cavity ultrafast thulium-doped fiber lasers and verified that the properties of the generated mode-locked pulses match well with the U-DSAD characteristics found in the numerical study. The best-performing laser generated a peak power of 330 kW and a maximum pulse energy of 80 nJ with a pulse duration of 249 fs at a repetition rate of 428 kHz. Such a high peak power exceeds that of any previous mode-locked pulses generated from a single-mode fiber laser without post-treatment. We anticipate that the means to overcome cubic nonlinearity presented in this paper can give insight in various optical fields dealing with nonlinearity to find solutions beyond the inherent limitations.