We present the validation of two TESS super-Earth candidates transiting the mid-M dwarfs TOI-6002 and TOI-5713 every 10.90 and 10.44 days, respectively. The first star (TOI-6002) is located 32.038 ± 0.019 pc away, with a radius of 0.2409‑0.0065+0.0066 R⊙, a mass of 0.2105‑0.0048+0.0049 M⊙, and an effective temperature of 3229‑57+77 K. The second star (TOI-5713) is located 40.946 ± 0.032 pc away, with a radius of 0.2985‑0.0072+0.0073 R⊙, a mass of 0.2653 ± 0.0061 M⊙, and an effective temperature of 3225‑40+41 K. We validated the planets using TESS data, ground-based multi-wavelength photometry from many ground-based facilities, as well as high-resolution AO observations from Keck/NIRC2. TOI-6002 b has a radius of 1.65‑0.19+0.22 R⊕ and receives 1.77‑0.110.16S⊕. TOI-5713 b has a radius of 1.77‑0.11+0.13 R⊕ and receives 2.42 ± 0.11S⊕. Both planets are located near the radius valley and near the inner edge of the habitable zone of their host stars, which makes them intriguing targets for future studies to understand the formation and evolution of small planets around M-dwarf stars.