  Motivated by the LHCb Collaboration's observation of a doubly charmed
tetraquark state $T_{cc}(3875)$, we systematically investigate the existence of
doubly charmed pentaquark states using the resonating group method based on the
QDCSM framework. The effective potential of the two involved hadrons and the
bound state dynamics are included in the present work. Moreover, we have also
calculated the scattering phase shifts of open channels by channel coupling to
look for possible resonance states. Our estimations indicate that there is a
bound state in $I(J^{P})=\frac{3}{2}(\frac{5}{2}^{-})$, with a mass of $4461.7$
MeV. Additionally, five resonance states can be obtained by coupling the open
channel, which are $\Xi_{cc}\rho$ and $\Sigma_{c}D^{\ast}$ with
$I(J^{P})=\frac{1}{2}(\frac{1}{2}^{-})$, $\Lambda_{c}D^{\ast}$ and
$\Sigma_{c}D^{\ast}$ with $I(J^{P})=\frac{1}{2}(\frac{3}{2}^{-})$ and
$\Sigma_{c}D^{\ast}$ with $I(J^{P})=\frac{3}{2}(\frac{1}{2}^{-})$respectively.
The existence of these predicted doubly charmed pentaquark states needs to be
supported by experimental measurements and discoveries. We hope that some
experiments can find evidence of these states.
