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Using data samples with a total integrated luminosity of 253 pb-1 collected by the BESIII detector operating at the BEPCII collider, the differential cross sections of inclusive π± and K± production, as a function of the momentum and normalized by the total hadronic cross section, are measured at center-of-mass energies from 2.000 to 3.671 GeV. The measured π± cross sections are consistent with the previously reported π0 cross sections by BESIII, while the K± cross sections are systematically higher than the KS0 cross sections by a factor of approximately 1.4. These new results are in agreement with state-of-the-art QCD analyses at next-to-next-to-leading-order accuracy, particularly in the large hadron momentum region at energy scales down to 3 GeV. These findings support the validity of isospin symmetry in parton fragmentation processes.