The easiest way to do that:
make an unzipped version of the addon you want to package with it,
plop into gamemode dolder
make server.cs, and in the file, put
exec("./Script_whatever/server.cs");
put server.cs into gamemode folder
make sure that script is in the gamemode zip!
in gamemode.txt, add
ADDON Gamemode_SpeedDM
that should be all
if you need more, just repeat same process and just addon to server.cs
Final product
in Gamemode_SpeedDM
server.cs
Script_Whatever (UNZIPPED)
gamemode.txt
other gamemode stuff...