  We compute a model-independent correlation between the difference of
neutron-neutron and proton-proton scattering lengths |a(nn)-a^C(pp)| and the
splitting in binding energies between Helium-3 and tritium nuclei. We use the
effective field theory without explicit pions to show that this correlation
relies only on the existence of large scattering lengths in the NN system. Our
leading-order calculation, taken together with experimental values for binding
energies and a^C(pp), yields a(nn)=-22.9 \pm 4.1 fm.
