Volumetric breaks at mesh intersection

[phoenixart]

I'm sure I'm doing this wrong. I've updated the Cube shader like so:

I don't want to keep bugging you with newbie questions. If there's a tutorial I'll take a look (I couldn't find any so far..)

[B.Y.O.B.]

Put your homogeneous fog volume node into an own volume node tree (like the camera volume you have now).
Then use a pointer node to refer to this fog volume both as interior volume of the fog cube and as exterior volume of the camera.

[phoenixart]

Put your homogeneous fog volume node into an own volume node tree (like the camera volume you have now).

Which I assume would be something like this (not assigned to anything in the scene)

Then use a pointer node to refer to this fog volume both as interior volume of the fog cube[...]

This for the interior:

[...] and as exterior volume of the camera.

And here I'm not following.
When I add the pointer to the camera volume I don't see an exterior node socket:

[B.Y.O.B.]

And here I'm not following.
When I add the pointer to the camera volume I don't see an exterior node socket:

You can select CUBE_VOLUME in the camera volume dropdown.

[phoenixart]

Sorry for the delayed response, B.Y.O.B

Selecting CUBE_Volume in the camera volume dropdown did the trick.
Now the result is different from my initial setup, it looks darker and dimmed, but I guess it's just a matter of tweaking the settings in order to bring back more light into the scene.

Thanks again for guiding me through this setup.