  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, pi1(1400) and pi1(1600), which couple separately to eta pi and eta'
pi. 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 eta(') pi 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 pi1 resonant pole, with mass and width 1564 +- 24 +- 86 MeV
and 492 +- 54 +- 102 MeV, which couples to both eta(') pi channels. We find no
evidence for a second exotic state. We also provide the resonance parameters of
the a2(1320) and a2'(1700).
