  We report the most precise determination of the $^{1}S_{0}$ neutron-neutron
effective range parameter ($r_{nn}$) from neutron-neutron quasifree scattering
in neutron-deuteron breakup. The experiment setup utilized a collimated beam of
15.5 MeV neutrons and an array of eight neutron detectors positioned at angles
sensitive to several quasifree scattering kinematic configurations. The two
neutrons emitted from the breakup reaction were detected in coincidence and
time-of-flight techniques were used to determine their energies. The
beam-target luminosity was measured in-situ with the yields from
neutron-deuteron elastic scattering. Rigorous Faddeev-type calculations using
the CD Bonn nucleon-nucleon potential were fit to our cross-section data to
determine the value of $r_{nn}$. The analysis was repeated using a semilocal
momentum-space regularized N$^4$LO$^+$ chiral interaction potential. We
obtained values of $r_{nn} = 2.86 \pm 0.01 \,(stat) \pm 0.10 \,(sys)$ fm and
$r_{nn} = 2.87 \pm 0.01 \,(stat) \pm 0.10 \,(sys)$ fm using the CD Bonn and
N$^4$LO$^+$ potentials, respectively. Our results are consistent with charge
symmetry and previously reported values of $r_{nn}$.
