  A careful reanalysis is made on $e^+e^-\to X(4660)\to
(\Lambda_c\bar{\Lambda}_c)/(\psi'\pi\pi)$ processes, aiming at resolving the
apparent conflicts between Belle and BESIII data above
$\Lambda_c\bar{\Lambda}_c$ threshold. We use a model containing a Breit-Wigner
resonance and $\Lambda_c\bar{\Lambda}_c$ four-point contact interactions, with
which the enhancement right above the $\Lambda_c\bar{\Lambda}_c$ threshold is
well explained by a virtual pole generated by $\Lambda_c\bar{\Lambda}_c$
attractive final state interaction, located at $M_V=4.566\pm0.007$ GeV.
Meanwhile, $X(4660)$ remains to be a typical Breit-Wigner resonance, and is
hence of confinement nature. Our analysis strongly suggests the existence of
the virtual pole with statistical significance of $4.2$ standard deviation
($\sigma$). Nevertheless, the conclusion crucially depends on the line-shape of
cross sections which are of limited statistics, hence we urge new experimental
analyses from Belle II, BESIII, and LHCb to settle the issue.
