Give your enemy multiple targets. Try to divide your units into different 'regiments' and attack from different directions. More targets means you're hitting less at once, and you're microing on your attack there.
For the mines, there's a few things you can do.
If you get speedlots, try to rush toward their tanks while avoiding the mines so when they do explode, it'll at least deal some damage to their units as well.
If that isn't an option, make sure you send in zealots with goons behind them.
If your enemy has sieged tanks and vulture mines though, I'm willing to bet this is a little more than 7 mins into the game considering it's about a minute to research both, let alone aquire the gas to build a Factory, machine shop, and the tanks to be seiged.
I know this isn't the world's greatest suggestion for strategy, but if they're really turtled, another option would be avoiding them altogether and dropping in their base. If they've spent all that money on outer base defense, show them how weak their infrastructure is on the inside. While they're building tanks and sending them to the front, send some zealots and goons near their CC and start taking out the SCVs. 2-3 well microed shuttle-dropped units can do some serious damage to a Terran player with everything on the other side of their base.
Just keep the shuttles by if you see you're getting outnumbered and outgunned fast.
High Templar are always nice too.
