We present a strategy to extract the position of the two Lambda(1405) poles from experimental photoproduction data measured recently at different energies in the gamma p -> K+pi(0)Sigma(0) reaction at Jefferson Laboratory. By means of a chiral dynamics motivated potential with free parameters, we solve the Bethe-Salpeter equation in the coupled channels (K) over barN and pi Sigma in isospin I = 0 and parametrize the amplitude for the photonuclear reaction in terms of a linear combination of the pi Sigma -> pi Sigma and (K) over barN -> pi Sigma scattering amplitudes in I = 0, with a different linear combination for each energy. Good fits to the data are obtained with some sets of parameters, by means of which one can also predict the cross section for the K- p -> pi(0)Sigma(0) reaction. These later results help us decide among the possible solutions. The result is that the different solutions lead to two poles similar to those found in the chiral unitary approach. With the best result we find the two Lambda(1405) poles at 1385 ¿ 68i MeV and 1419 ¿ 22i MeV.