The LHCb Collaboration has recently observed two narrow baryon resonances with beauty. Their masses and decay modes look consistent with the quark model orbitally excited states Lambda(b)(5912) and Lambda(b)*(5920), with quantum numbers J(P) = 1/2(-) and 3/2(-), respectively. We predict the existence of these states within a unitarized meson-baryon coupled-channel dynamical model, which implements heavy-quark spin symmetry. Masses, quantum numbers and couplings of these resonances to the different meson-baryon channels are obtained. We find that the resonances Lambda(0)(b)(5912) and Lambda(0)(b)(5920) are heavy-quark spin symmetry partners, which naturally explains their approximate mass degeneracy. Corresponding bottom-strange baryon resonances are predicted at Xi(b)(6035.4) (J(P) = 1/2(-)) and Xi(b)(6043.3) (J(P) = 3/2(-)). The two Lambda(b) and two Xi(b) resonances complete a multiplet of the combined symmetry SU(3)-flavor times heavy-quark spin.