The Dalitz plot analysis technique is used to study the resonant substructures of B− → Dþπ−π− decays in a data sample corresponding to 3.0 fb−1 of pp collision data recorded by the LHCb experiment during 2011 and 2012. A model-independent analysis of the angular moments demonstrates the presence of resonances with spins 1, 2 and 3 at high Dþπ− mass. The data are fitted with an amplitude model composed of a quasi-model-independent function to describe the Dþπ− S wave together with virtual contributions from the Dð2007Þ0 and B0 states, and components corresponding to the D 2ð2460Þ0, D1ð2680Þ0, D3ð2760Þ0 and D2ð3000Þ0 resonances. The masses and widths of these resonances are determined together with the branching fractions for their production in B− → Dþπ−π− decays. The Dþπ− S wave has phase motion consistent with that expected due to the presence of the D0ð2400Þ0 state. These results constitute the first observations of the D3ð2760Þ0 and D2ð3000Þ0 resonances, with significances of 10σ and 6.6σ, respectively.