In order to reveal many-body interactions in the three-dimensional (3D) perovskite manganite, we have performed an $in$ $situ$ angle-resolved photoemission spectroscopy (ARPES) on La$_{0.6}$Sr$_{0.4}$MnO$_3$ (LSMO) and investigated the behaviors of quasiparticles. We observe quasiparticle peaks around the Fermi momentum, both in the electron and the hole bands, and clear kinks throughout the hole Fermi surface in the ARPES band dispersion. The isotropic behavior sharply contrasts to the strong anisotropic quasiparticle excitation observed in layered manganites. These results suggest that polaronic quasiparticles by coupling of the electrons with Jahn-Teller phonons play an important role in the physical properties of the ferromagnetic metallic phase in 3D manganite LSMO.