감칠맛 sometimes can be translated to umami.

Savory taste. Maybe 감칠맛 in that sentence means 'harmony beyond words.' 각본을 써준 작가님과 굉장히 감칠맛 나게 작업했다. = Worked in harmony-beyond-words with the writer who wrote the script. 감칠맛 is unique word in Korea - which can't wholly translated to English. It is kind of 맛(taste), but unlike other kinds, it is more used as that way in the sentence above. I think best way to understand 감칠맛 is to look, listen and speak a lot of expressions that contains 감칠맛, not trying to translate, since it is such a unique word.