We report (formula presented) NMR studies that address the underlying two superconducting (SC) gaps model and a possible mechanism for interpreting a high SC transition temperature (formula presented) of (formula presented) in a recently discovered (formula presented) We reported in a previous paper [Phys. Rev. Lett. (formula presented) 127001 (2001)] that the results of the nuclear-spin-lattice relaxation rate, (formula presented) in the SC state revealed the existence of a single large SC gap with (formula presented) This conclusion is corroborated by the calculation that any two-gap models cannot account for the experimental results. In Al-doped (formula presented) the result of (formula presented) in the SC state revealed that a size in the SC gap is not changed by substituting Al for Mg. The reduction in (formula presented) by Al doping is shown to be due to the decrease of the density of states (formula presented) at the Fermi level. According to the McMillan equation, an experimental relation between (formula presented) and the relative change in (formula presented) allowed us to estimate a characteristic phonon frequency (formula presented) and an electron-phonon coupling constant (formula presented) These results suggest that the high- (formula presented) superconductivity in (formula presented) is mediated by the strong electron-phonon coupling with high-frequency phonons. © 2002 The American Physical Society.