I've experienced a problem when a strange situation is happening - I can only add/remove items to cart using the base URL. Works:

<base_url>/?addtocart=10 | <base_url>/?remove_item=<item_key>&_wpnonce=<nonce>  

Doesn't work:

<base_url>/<cart_slug>/?addtocart=10 | <base_url>/<cart_slug>/?remove_item=<item_key>&_wpnonce=<nonce>  

Any idea why it works that way?