We report on unprecedentedly large coupled cluster calculations for the C₆₀⁻ anion, and on a heuristic model uncovering the valence states of C₆₀⁻ that allow the resolution of the headlined question. Our results convincingly demonstrate that C₆₀⁻ possesses as many as four bound valence states: ²T_1u, ²T_1g, ²T_2u and ²H_g. Our findings reconcile previous controversies regarding the existence of the bound ²T_2u and ²H_g states. For all bound states of C₆₀⁻ we present an analysis of the radial and angular distributions of the excess electron, which reveals some unique properties of the valence states. Some interesting features of the introduced model are analyzed and discussed.