The ²⁴⁶Cm(n,γ) and ²⁴⁸Cm(n,γ) cross-sections have been measured at the Experimental Area 2 (EAR2) of the n_TOF facility at CERN with three C₆D₆ detectors. This measurement is part of a collective effort to improve the capture cross-section data for Minor Actinides (MAs), which are required to estimate the production and transmutation rates of these isotopes in light water reactors and innovative reactor systems. In particular, the neutron capture in ²⁴⁶Cm and ²⁴⁸Cm open the path for the formation of other Cm isotopes and heavier elements such as Bk and Cf and the knowledge of (n,γ) cross-sections of these Cm isotopes plays an important role in the transport, transmutation and storage of the spent nuclear fuel. The reactions ²⁴⁶Cm(n,γ) and ²⁴⁸Cm(n,γ) have been the two first capture measurements analyzed at n_TOF EAR2. Until this experiment and two recent measurements performed at J-PARC, there was only one set of data of the capture cross-sections of ²⁴⁶Cm and ²⁴⁸Cm, that was obtained in 1969 in an underground nuclear explosion experiment. In the measurement at n_TOF a total of 13 resonances of ²⁴⁶Cm between 4 and 400 eV and 5 of ²⁴⁸Cm between 7 and 100 eV have been identified and fitted. The radiative kernels obtained for ²⁴⁶Cm are compatible with JENDL-5, but some of them are not with JENDL-4, which has been adopted by JEFF-3.3 and ENDF/B-VIII.0. The radiative kernels obtained for the first three ²⁴⁸Cm resonances are compatible with JENDL-5, however, the other two are not compatible with any other evaluation and are 20 and 60% larger than JENDL-5.