We present the first ever measurements of femtoscopic correlations between the K_S ⁰ and K^± particles. The analysis was performed on the data from Pb–Pb collisions at s_NN=2.76 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding via the a₀(980) resonance. The extracted kaon source radius and correlation strength parameters for K_S ⁰K⁻ are found to be equal within the experimental uncertainties to those for K_S ⁰K⁺. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the a₀ resonance are tested. Our results are also compatible with the interpretation of the a₀ having a tetraquark structure instead of that of a diquark.