  We use an existing model of the $\Lambda\Lambda N - \Xi NN$ three-body system
based in two-body separable interactions to study the $(I,J^P)=(1/2,1/2^+)$
three-body channel. For the $\Lambda\Lambda$, $\Xi N$, and $\Lambda\Lambda -
\Xi N$ amplitudes we have constructed separable potentials based on the most
recent results of the HAL QCD Collaboration. They are characterized by the
existence of a resonance just below or above the $\Xi N$ threshold in the
so-called $H$-dibaryon channel, $(i,j^p)=(0,0^+)$. A three-body resonance
appears {2.3} MeV above the $\Xi d$ threshold. We show that if the
$\Lambda\Lambda - \Xi N$ $H$-dibaryon channel is not considered, the
$\Lambda\Lambda N - \Xi NN$ $S$ wave resonance disappears. Thus, the possible
existence of a $\Lambda\Lambda N - \Xi NN$ resonance would be sensitive to the
$\Lambda\Lambda - \Xi N$ interaction. The existence or nonexistence of this
resonance could be evidenced by measuring, for example, the $\Xi d$ cross
section.
