Electronic structure of the three-dimensional colossal magnetoresistive perovskite ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ has been established using soft-x-ray angle-resolved photoemission spectroscopy with its intrinsically sharp definition of three-dimensional electron momentum. The experimental results show much weaker polaronic coupling compared to the bilayer manganites and are consistent with the theoretical band structure including the empirical Hubbard parameter U. The experimental Fermi surface unveils the canonical topology of alternating three-dimensional electron spheres and hole cubes, with their shadow contours manifesting the rhombohedral lattice distortion. This picture has been confirmed by one-step photoemission calculations including displacement of the apical oxygen atoms. The rhombohedral distortion is neutral to the Jahn-Teller effect and thus polaronic coupling, but affects the double-exchange electron hopping and thus the colossal magnetoresistance effect.