Possible Solutions:
6, 9, 11, 12, 4, 14, 7
8, 7, 13, 10, 6, 12, 9
Explanation:
You could do it by repeatedly guessing, but that won't determine you have found all the solutions.
First, I listed down all the possible sums. For example, for clue 1, I listed sown all the numbers that added up to 15 (1+14, 2+13, etc).
Then, you link the sums. For example, if you had, let's say 6+9 in the first list, and there was, 9+11 on the second list, you link those two and only write the common number that appears in boths lists down once. Don't forget, that number is the breakpoint between the two sums.
After you have finished listing the solutions, proof-read it over again for repeated numbers or numbers that don't add together to make the right number.
You should manage to end up with the two solutions I had.