Yes, you were correct on the first part. And the rest means ===>> but I cannot go there next week.
담주엔< 다음 주엔 < 다음 주에는 = next week
못 간답니다 is from 못 간다, 못 갑니다 = 못-(cannot) 간다(go or come)
Now can you see the contractions?? because of many short versions of phrases, it will be hard to get the exact meaning through dictionsary.