An angular analysis of B degrees -> J/psi K+pi(-) decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 fb(-1) collected with the LHCb detector. The m(K+pi(-) ) spectrum is divided into fine bins. In each m(K+pi(-)) bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by K* resonances is examined, making minimal assumptions about the K+pi(-) system. The data reject the K*-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the m(J/psi pi(-)) vs m(K+pi(-)) plane suggests structures near m(J/psi pi(-)) = 4200 and 4600 MeV.