Also tightly sealed isn't the issue if it's not lit.
You need to light a place to ensure no monsters spawn inside. Then seal it so they can't wander into your safe zone.
My stuff is very controlled. They spawn where I want. Note that slimes will spawn around y = 16 in certain chunks lit up or not. They are the exception. Only one in 13 chunks can spawn slimes so you can take that as good luck if you can identfy the borders (16x16x128 chunks) and build a significant cage for them to spawn in (fully lit).