Need help for deleting a WordPress Cookie with setcookie() Not Working

I'm currently working on a WordPress plugin where I've set a cookie on the front end using PHP's setcookie() function. However, I'm encountering an issue when trying to delete the cookie using setcookie($cookie_name, '', time()-3600, '/'). It doesn't seem to work as expected, and the cookie persists. Can someone please help me understand what might be causing this problem and how to properly delete the cookie?