An accurate measurement of the ¹⁴⁰Ce(n,ү) energy-dependent cross-section was performed at the n_TOF facility at CERN. This cross-section is of great importance because it represents a bottleneck for the s-process nucleosynthesis and determines to a large extent the cerium abundance in stars. The measurement was motivated by the significant difference between the cerium abundance measured in globular clusters and the value predicted by theoretical stellar models. This discrepancy can be ascribed to an overestimation of the ¹⁴⁰Ce capture cross-section due to a lack of accurate nuclear data. For this measurement, we used a sample of cerium oxide enriched in ¹⁴⁰Ce to 99.4%. The experimental apparatus consisted of four deuterated benzene liquid scintillator detectors, which allowed us to overcome the difficulties present in the previous measurements, thanks to their very low neutron sensitivity. The accurate analysis of the p-wave resonances and the calculation of their average parameters are fundamental to improve the evaluation of the ¹⁴⁰Ce Maxwellian-averaged cross-section.