Successfully redirect non-www url to www url but site doesn't pull up (Ubuntu 14.04 Nignx LEMP)

Hi, I managed to successfully forward non-www to www address on my site. So if I type website.com it’ll automatically go to www.website.com.

However, the site doesn’t pull up anything. It shows error “Server not found” “Browser can’t find the server at www.website.com.” When I type in the IP address, it pulls up just fine.

BTW, I’m very newbie to using Ubuntu and building a server from scratch like this (DigitalOcean style), so any help is appreciated. I searched through articles and questions in Community section but none of the answers manage to get the site to pull up.

This is my virtualhost file setting:

server {
     listen 80;
     server_name website.com;
     return 301 $scheme://www.website.com$request_uri;
}

server {
     listen 80 default_server;
     listen [::]:80 default_server ipv6only=on;
     root /var/www/website.com/html;
     server_name www.website.com;
     ............the rest of the code settings...........
     ...................
}

I then restarted nginx with

sudo service nginx restart

I also set up the DNS to be:

@ A 111.111.111.11
@ AAAA 1111:1111::1111:(the IPv6 address, basically)
www CNAME @

Help? Thanks in advance!