For a full clarification of how AJAX works inside WordPress, you should Check out the Codex here. For A fast overview of how I solved this certain difficulty, read on:
NOTE: if you want support utilizing this function https://bronteaxwz355544.pointblog.net/the-smart-trick-of-woocommerce-update-mini-cart-quantity-ajax-that-no-one-is-discussing-71088629