How to show that two integers with a sum of zero have one's complement representations that are bit-complementary?

I've been stuck on this question for a while now:

Show mathematically that two integers that have a sum of zero have one’s complement representations that are bit-complementary.

Here is a simple proof and a counter example:

One's complement representation by definition represents negative values with bit-complement. In other words -n is represented as ~n. If any two integers have a sum of zero, either they are both zero or one is the opposite of the other.

• if they are both zero, they do not necessarily have one’s complement representations that are bit-complementary.
• if they are opposite of each other and non-zero, then yes, they are bit-complementary of one another.