  We discuss the mass splittings for the $S$-wave triply heavy pentaquark
states with the $QQQq\bar{q}$ $(Q=b,c;q=u,d,s)$ configuration which is a mirror
structure of $Q\bar{Q}qqq$. The latter configuration is related with the nature
of $P_c(4380)$ observed by the LHCb Collaboration. The considered pentaquark
masses are roughly estimated with a simple method. One finds that such states
are probably not narrow even if they do exist. This leaves room for molecule
interpretation for a state around the low-lying threshold of a doubly heavy
baryon and a heavy-light meson, e.g. $\Xi_{cc}D$, if it were observed. As a by
product, we conjecture that upper limits for the masses of the conventional
triply heavy baryons can be determined by the masses of the conventional doubly
heavy baryons.
