  We investigate the sensitivity of the three-nucleon system to changes in the
neutron-neutron scattering length to next-to-leading order in the pionless
effective field theory, focusing on the the triton-3He binding energy
difference and neutron-deuteron elastic scattering. Due to the appearance of an
electromagnetic three-body counterterm at this order, the triton-3He binding
energy difference remains consistent with the experimental value even for large
positive neutron-neutron scattering lengths while the elastic neutron-deuteron
scattering phase shifts are insensitive. We conclude that a bound dineutron
cannot be excluded to next-to-leading order in pionless EFT.
