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<?php
add_filter('query_vars', function($vars){
    array_push($vars, 'my_meta_key');
    return $vars;
});
add_action('restrict_manage_posts', function(){
    printf(
        '<input type="text" id="%1$s" name="%1$s" value="%2$s" />',
        'my_meta_key',
        esc_attr(get_query_var('my_meta_key'))
    );
});
add_filter('posts_where', function( $where ) {
    global $wpdb;
    if ( !is_admin() )
        return $where;
    $value = get_query_var('my_meta_key');
    if ( !empty($value) ) {
        $where .= $wpdb->prepare("
             AND EXISTS (
             SELECT 'x'
             FROM {$wpdb->postmeta} as m
             WHERE m.post_id = {$wpdb->posts}.ID 
             AND m.meta_key = 'my_meta_key'
             AND m.meta_value like %s
            )",
            "%{$value}%"
        );
    }
    return $where;
});