  We study the spectrum of the isoscalar pentaquark $udsc\overline{c}$, of
either positive or negative parity, in a constituent quark model with linear
confinement and a flavor-spin hyperfine interaction previously extended to
SU(4) and used to describe the spectrum of the $uudc\overline{c}$ pentaquarks
observed at LHCb in 2019. For positive parity we make a distinction between the
case where one unit of angular momentum is located in the subsystem of four
quarks and the case where the angular momentum is located in the relative
motion between a ground state four-quark subsystem and the antiquark. The
novelty is that we introduce the coupling between different flavor states, due
to the breaking of exact SU(4)-flavor symmetry of the Hamiltonian model, both
for positive and negative parity states. An important consequence is that the
lowest state, located at 4404 MeV, has quantum numbers $J^P$ = $1/2^-$ while
without coupling the lowest state has $J^P$ = $1/2^+$ or $3/2^+$.
