It will modify the quantity & calculate the total of the cart

ajax_function.php

<?php
function update_order_review() {
  $values = array();
  parse_str($_POST['post_data'], $values);
  $cart = $values['cart'];
  foreach ( $cart as $cart_key => $cart_value ){
      WC()->cart->set_quantity( $cart_key, $cart_value['qty'], false );
      WC()->cart->calculate_totals();
      woocommerce_cart_totals();
  }
  wp_die();
}