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We employ Mn L₃-edge Resonant Inelastic X-ray Scattering (RIXS) to investigate the collective spin excitations in ferromagnetic metallic La_2/3Ca_1/3MnO₃ (LCMO) thin film. With the benefit of high-resolution RIXS, we find a bulk-like ferromagnon dispersion along [h,h,h] which at low Q is consistent with prior neutron scattering results on single crystals. Importantly, extending Q above 0.3 r.l.u., where no neutron data are available, reveals a zone-boundary magnon flattening along [h,h,h]. We describe the magnon dispersion using the Heisenberg model with next-nearest-neighbor exchange coupling. The combination of our data and theory enables settling the inconsistency between neutron data and multiple theoretical approaches. In addition, above 70 meV, we identify a Mn-O stretching phonon, a higher order multi-phonon, and a bi-magnon modes. The visualization of all these excitations leads us to evaluate the spin-phonon coupling. Indeed, spin-phonon coupling is evidenced near the zone center along [h,h,h], with the mutual renormalization of the Jahn-Teller active phonon and the single spin-flip magnon, as well as damping of the magnon. Our results extend the knowledge of the elementary excitations of LCMO shedding light on the long-standing problem of its magnetic interactions.