Probably out of alignment or could be the shocks or like you said, tie rod which holds the tires together. The fact that it shakes when you are going that fast probably means something but I don't know what. Check out this website and they probably have a specific answer.
http://www.cartalk.com/
EXCERPT FROM SHOW:
Dear Tom and Ray:
I have a '76 Capri. At about 35 mph on a left turn, the front end shimmies. It doesn't shimmy at any other time. It seems that the right front dips down when it happens and the right front shock seems a little soft. Could a weak shock cause this condition? Ethel
Ray: It's possible, but unlikely, Ethel. But since it's a 1976 Capri, we can't rule out anything. You could have a weak shock, a weak spring, or a grossly underinflated tire. But it could easily be something much worse. The right front wheel might be getting ready to fall off.
Tom: So--as with all other shimmies and shakes in the front end--it's imperative that you get a mechanic to give the front end a very thorough inspection.
Ray: If I had to guess, I'd say the most likely cause of this type of shimmy is a bad tie rod end. The tie rods are the metal rods that actually push and pull the front wheels when you turn the steering wheel. At the end of each tie rod, there are ball and socket joints called tie rod ends. And if one of the tie rod ends wears out, it could allow that wheel to wobble under certain conditions...like when you drive! But that's not the worst of it. If one of these tie rod ends breaks, you lose complete control of the car.
Tom: So you absolutely must get it looked at soon by a good mechanic. I realize this is only a beat up, old '76 Capri, and you probably don't have any feelings for it anymore, Ethel. But think about all the NICE cars you might smash into if the tie rod end does break! 1215