  We derive the holographic entanglement entropy functional for a generic
gravitational theory whose action contains terms up to cubic order in the
Riemann tensor, and in any dimension. This is the simplest case for which the
so-called splitting problem manifests itself, and we explicitly show that the
two common splittings present in the literature - minimal and non-minimal -
produce different functionals. We apply our results to the particular examples
of a boundary disk and a boundary strip in a state dual to 4-dimensional
Poincar\'e AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement
surface for both functionals and finding that causal wedge inclusion is
respected for both splittings and a wide range of values of the cubic coupling.
