You are missing a default route.

In ubuntu, you'll need:

 gateway <IP of default route>

Here is /etc/network/interfaces on my system (with a private IP, but there is no difference):

auto eth0
iface eth0 inet static
    address 10.22.16.2
    netmask 255.255.255.0
    network 10.22.16.0
    broadcast 10.22.16.255
    gateway 10.22.16.1
    # dns-* options are implemented by the resolvconf package, if installed
    dns-nameservers 10.21.1.21
    dns-search example.com

Default Gateways work a bit differently on IPv6.

What I suggest you do is fire up tcpdump and watch it for Router Advertisements (you might want to analyse the capture in WireShark - much easier). This is how your IPv6 host knows how to get out to the internet. Also watch for Neighbor Solicitation as this is the replacement for ARP.

If you see these requests coming in, but not going back out, then your internal firewall is blocking IPv6 traffic. If you see them going out (requests), but not back in, then you need to make sure that your prefix length is correct (that's the /64 part. Although I've seen a lot of /64s being passed out that are actually a /48).

Big Important Bold Bit

ICMP is absolutally critical for IPv6 functionality. In IPv4 it can be blocked without huge impact, but in IPv6, the whole network relies on ICMP for all its functionality. Don't block it.

In reference to

My provider gave me a "/64" (whatever that is - I'm still confused) of IPv6 addresses

That's your Prefix Length, previously known as your Subnet Mask that's used for CIDR. The lower the number, the more IP addresses you have. For IPv6, /64 and /48 are very common and should give you more IP addresses than you will ever need in your entire life.