A common workaround is to use Excel Solver. But it has two major limitations:
* It can only handle up to around 70 numbers at a time;
* It supports only one target sum at a time.
So, I developed a Google Sheets add-on called "Add Up To" in the hope of solving the problem and all similar ones.
If you're facing the same challenge, check it out at https://workspace.google.com/marketplace/app/add_up_to/10202...
It's completely free for now and may become a paid add-on with a one-off fee in the future when it becomes more mature.