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Lead-halide perovskite (LHP) semiconductors are emergent optoelectronic materials with outstanding transport properties which are not yet fully understood. We find signatures of large polaron formation in the electronic structure of the inorganic LHP CsPbBr$_3$ by means of angle-resolved photoelectron spectroscopy. The experimental valence band dispersion shows a hole effective mass $0.26\pm0.02\,\,m_e$, 50% heavier than the bare mass $m_0 =0.17 m_e$ predicted by density functional theory. Calculations of electron-phonon coupling indicate that phonon dressing of the carriers mainly occurs via distortions of the Pb-Br bond with a Fr\"ohlich coupling parameter $\alpha=1.82$. A good agreement with our experimental data is obtained within the Feynmann polaron model, validating a viable theorical method to predict the carrier effective mass of LHPs ab-initio.