Install and run subl from .deb file on a headless server

Basically I just want to be able to do this:

ssh -fX server.example.com subl -w

But after installing Sublime Text 3 from the .deb file on a headless Ubuntu server, subl fails to run, printing out many lines about missing libraries:

$ subl 2>&1 | awk '{ print $NF }' | sort | uniq
libcairo.so<br>libgdk-x11-2.0.so
libgtk-x11-2.0.so
libpango-1.0.so
libpangocairo-1.0.so

I can manually install the depencies with:

$ sudo apt-get install libcairo2 libgtk2.0-0 libpango1.0-0

Then it works. But it would be easier if the depencies were listed in the .deb file, so I don't have to figure out the names of all the required packages each time I install Sublime Text on a new server.

As you can see, there are no dependencies listed currently:

$ dpkg-deb --info sublime-text_build-3059_amd64.deb 
 new debian package, version 2.0.
 size 6253946 bytes: control archive= 313 bytes.
     247 bytes,     8 lines      control              
 Package: sublime-text
 Version: 3059
 Architecture: amd64
 Maintainer: Sublime HQ <support@sublimetext.com>
 Section: editors
 Priority: optional
 Description: Sublime Text is a sophisticated text editor for code, markup and prose
 Installed-Size: 14200