Mapping states with explicit gluonic degrees of freedom in the light sector is a challenge, and has led to controversies in the past. In particular, the experiments have reported two different hybrid candidates with spin-exotic signature, π_{1}(1400) and π_{1}(1600), which couple separately to ηπ and η^{'}π. This picture is not compatible with recent Lattice QCD estimates for hybrid states, nor with most phenomenological models. We consider the recent partial wave analysis of the η^{(')}π system by the COMPASS Collaboration. We fit the extracted intensities and phases with a coupled-channel amplitude that enforces the unitarity and analyticity of the S matrix. We provide a robust extraction of a single exotic π_{1} resonant pole, with mass and width 1564±24±86 and 492±54±102 MeV, which couples to both η^{(')}π channels. We find no evidence for a second exotic state. We also provide the resonance parameters of the a_{2}(1320) and a_{2}^{'}(1700).