How to refresh cart item quantity using Ajax API?

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Hi,

I'm running the Ajax cart API for adding a new item to the cart over my app embed, I see the operation has been succeeded by fetching the cart (via ajax API as well) , but I don't manage to update the cart's quantity.

I was looking for this issue and found many open discussions about it but never found solid answer that. It is important for me to emphasize that the solution needs to be generic for all/most of Shopify's themes.

Thanks