  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 $32.038\pm0.019$ pc away, with a radius of
$0.2409^{+0.0066}_{-0.0065} R_\odot$, a mass of $0.2105^{+0.0049}_{-0.0048}
M_\odot$ and an effective temperature of $3229^{+77}_{-57}$ K. The second star
(TOI-5713) is located $40.946\pm0.032$ pc away, with a radius of
$0.2985^{+0.0073}_{-0.0072} R_\odot$, a mass of $0.2653\pm0.0061 M_\odot$ and
an effective temperature of $3225^{+41}_{-40}$ 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 $1.65^{+0.22}_{-0.19} R_\oplus$ and
receives $1.77^{+0.16}_{-0.11} S_\oplus$. TOI-5713 b has a radius of
$1.77_{-0.11}^{+0.13} R_\oplus$ and receives $2.42\pm{0.11} S_\oplus$. 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.
