Get all posts with a certain meta key, except for one with specific title

Unable to test this at the moment, but try something along these lines. Search all posts for your Post Name (Special title), grabbing the ID’s, then utilize post__not_in to exclude those IDs in get_posts.

function getAllPostIdsTest(){

     global $wpdb;
     $excluded_posts = $wpdb->get_results("SELECT id FROM " . $wpdb->posts . " WHERE `post_title` LIKE '%"Special title"%' && `post_type` = 'post_test'");

     $args = array(
        'post_type' => 'post_test',
        'posts_per_page' => -1,
        'meta_query' => array(
            array(
                'key' => 'post_test_safe',
                'value' => 1,
                'compare' => '='
            ),
        ),
        'fields' => 'ids',
        'orderby' => 'asc',
        'post__not_in' => $excluded_posts
    );

    $ids = get_posts( $args );
    send_json($ids);

}

Edit: post__not_in is expecting a simple array of ID’s, ex// array(1,2,3,4)