Here is a brief description of how to determine the cage sums:
One of the cages @ r19c5,r37c28 must have the sum 19. Only the cage @ r7c2 is possible as all other 5 are 2-cell cages (max=8+9=17).
With that, the cages @ r7c46+r9c35 are either [7,1,3,17] or [2,4,16,12]
Also, r9c12=45-r9c34-r9c56-r9c789=45-38=7
=> r7c46+r9c1234=[71{34}{12}] or [24{16|25|34}{79}]
=> r9c56 must simultaneously see {347|479} no matter what
=> r9c56 can never be {39|48|57}
=> The cage @ r9c5 can't have a sum of 12
=> The cages @ r7c46+r9c35 must be [7,1,3,17]
Q.E.D.