Recent experimental progress has led to the detection of many new hadrons. Very recently, the LHCb Collaboration announced the observation of two new Sigma(b)(6097)(+/-) states in the Lambda(0)(b)pi(+/-) invariant mass distribution, which are considered to be the excited states of the ground-state Sigma((*))(b) baryon. Although almost all of the ground-state baryons have been observed, the fact that only a limited number of excited states have been observed makes them intriguing. Understanding the properties of the excited baryons would improve our knowledge about the strong interaction, as well as the nature and internal structures of these baryons. To specify the quantum numbers of the Sigma(+/-)(b(6097)) states, we analyze their strong decays to Lambda(0)(b) and pi(+/-) within the light-cone QCD sum rules formalism. To this end, they are considered as possible 1P or 2S excitations of either the ground-state Sigma(b) baryon with J = 1/2 or the Sigma(b)* baryon with J = 3/2, and their corresponding masses are calculated. The results of the analyses indicate that the Sigma(b)(6097)(+/-) baryons are excited 1P baryons with quantum numbers J(P) = 3-/2.