The 235U(n,f) cross section was measured in a wide energy range at n_TOF relative to 6Li(n,t) and 10B(n,alpha), with high resolution and in a wide energy range, with a setup based on a stack of six samples and six silicon detectors placed in the neutron beam. This allowed us to make a direct comparison of the reaction yields under the same experimental conditions, and taking into account the forward/backward emission asymmetry. A hint of an anomaly in the 10÷30 keV neutron energy range had been previously observed in other experiments, indicating a cross section systematically lower by several percent relative to major evaluations. The present results indicate that the evaluated cross section in the 9÷18 keV neutron energy range is indeed overestimated, both in the recent updates of ENDF/B-VIII.0 and of the IAEA reference data. Furthermore, these new high-resolution data confirm the existence of resonance-like structures in the keV neutron energy region. The new, high accuracy results here reported may lead to a reduction of the uncertainty in the 1÷100 keV neutron energy region. Finally, the present data provide additional confidence on the recently re-evaluated cross section integral between 7.8 and 11 eV.