  Fully correlated study of $_{\Lambda\Lambda} ^6$He hypernucleus has been
performed with two- and three- baryon potentials. For the S=-2 sector, various
simulations of Nijmegen $\Lambda\Lambda$ potential models have been used. We
investigate the role of every strength of the strange sector potentials on the
energy breakdown and present a crystal clear understanding of their interplay.
Consistency between $_\Lambda ^5$He and $_{\Lambda\Lambda}^6$He depends on the
$\Lambda N$ space-exchange strength only. Investigation limits the strength of
simulated Nijmegen $\Lambda\Lambda$ potential models. The study is a step
forward to determine all the strengths, to reslove A=5 anomaly and to search
for $_{\Lambda\Lambda}^4$H in an authentic way.
