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We demonstrate direct probing of strong magnon-photon coupling using Brillouin light scattering spectroscopy in a planar geometry. The magnonic hybrid system comprises a split-ring resonator loaded with epitaxial yttrium iron garnet thin films of 200 nm and 2.46 $μ$m thickness. The Brillouin light scattering measurements are combined with microwave spectroscopy measurements where both biasing magnetic field and microwave excitation frequency are varied. The cooperativity for the 200 nm-thick YIG films is 4.5, and larger cooperativity of 137.4 is found for the 2.46 $μ$m-thick YIG film. We show that Brillouin light scattering is advantageous for probing the magnonic character of magnon-photon polaritons, while microwave absorption is more sensitive to the photonic character of the hybrid excitation. A miniaturized, planar device design is imperative for the potential integration of magnonic hybrid systems in future coherent information technologies, and our results are a first stepping stone in this regard. Furthermore, successfully detecting the magnonic hybrid excitation by Brillouin light scattering is an essential step for the up-conversion of quantum signals from the optical to the microwave regime in hybrid quantum systems.