Try getting your wheels balanced first. Is the shake worse when braking at these speeds? My inclination would be to pay £5-£10 to get the wheels balanced and then seeing if the fault persists. Gearbox really wouldn't give these syptoms even if knackered.
I had a similar problem, it originally started in a fairly narrow range of speeds and felt like it was coming from the nearside front wheel, which made me think it was a problem with wheel balance and/or tracking, as suggested above.
However it kept getting worse, and I took it to my local garage who took it for a quick drive and initially guessed it was a part of the suspension that had broken or come loose.
Once they got it up on the lift, they found nothing wrong with any of the suspension components and tracked it down to the offside inboard CV joint which was starting to break up.
So I would check those things first before allowing anyone to pull the gearbox apart.
My garage had my car for just over an hour, and that included getting the replacement driveshaft deliverd from their supplier. So I would tend to agree that with that statement.
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