I can't add unbreakable tag to items with damage

What I expected to happen was...:
I expected to be able to summon an damaged item with the unbreakable tag. (I wanted the item to have damage because of a new Texture I made for it. )

What actually happened was...:
I summoned the item with the unbreakable tag and there wasn't any damage on the item.

Steps to Reproduce:
1. /summon minecraft:carrot_on_a_sick 1 1

{Unbreakable:1}