Update WooCommerce mini cart count via AJAX

functions.php

<?php

add_action('wp_ajax_cart_count', 'custom_cart_count');
add_action('wp_ajax_nopriv_cart_count', 'custom_cart_count');
function custom_cart_count() {
    echo WC()->cart->cart_contents_count;
    wp_die();
}

add_action('wp_enqueue_scripts', 'custom_scripts');
function custom_scripts()
{
    wc_enqueue_js( "
        $.ajax({
            url: '".admin_url('admin-ajax.php')."',
            data: {
                'action': 'cart_count'
            },
            success: function(resp) {
                $('REPLACE_WITH_COUNT_ELEMENT_SELECTOR').text(resp);
            }
        });
    ");
}