This is a combination of the words 感慨 meaning "strong feelings" and 深い meaning "deep." Something that makes you feel strong emotions deep down inside is deeply moving.
This is a combination of a jukugo word and an i-adjective. You've learned both of them so just mash them together, with the rendaku making ふ to ぶ, and you've got the reading down pat!
This is the first time my writing will be published, so of course it’s a deeply moving thing for me.