How to send a cookie after response.sendRedirect()?

I'm redirecting the user to some URL and I want to send a cookie with it:

        Cookie cookie = new Cookie("CADASTROADM", "someValue");
        cookie.setPath("/");
        cookie.setMaxAge(129600); //With it or without, makes no difference.
        URL urlToRedirect = new URL(pageToRedirect);
        cookie.setDomain(urlToRedirect.getHost());//With it or without, makes no difference.
        response.addCookie(cookie);
        response.sendRedirect(pageToRedirect);

However, when he's redirected to the page, the cookie is not there. I cannot use requestDispatcher.forward() because I'm redirecting the user to an absolute page.

Is it possible? What am I doing wrong?