  We study the hadronic coupling constants in the two-body strong decays of the
fully-charm tetraquark states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$
via the QCD sum rules based on rigorous quark-hadron duality. Then we obtain
the hadronic coupling constants and partial decay widths therefore total decay
widths, which support assigning the $X(6552)$ as the first radial excitation of
the scalar tetraquark state. And other predictions can be used to diagnose
exotic states in the future.
