In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x^{\text{'}}\left(t\right)\in -Ax\left(t\right)+f(t,x\left(t\right))$, $x\left(0\right)=x_0$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.