Right adjoints preserve j-dense monos

Question

Let’s assume $\epsilon$ is a topos and $L:\epsilon\longrightarrow \epsilon$ and $R:\epsilon \longrightarrow\epsilon$ are two adjoint functors such that $L\dashv R$. Now, let j be a Lawvere-Tierney topology in $\epsilon$. Let $m:M\longrightarrow M’$ be a j-dense mono. Now, since R preserves limits, it preserves pullbacks and I guess this gives us that $Rm:RM\longrightarrow RM’$ is also a j-dense mono. Is it true?