DAM were still making that reel as recently as the 80's. I well remember seeing them for sale.
Should you fish with it? Hmmmmm. In another post you say you are new to fly fishing...and trying to cast 11 foot of cane is going to be an experience
I still regularly fish cane, but for carp, but one thing I have learnt is that cane dries out over a period of time. That drying out makes the rods prone to cracking and breaking.
I personally would probably use it, but carefully! At 11 foot its probably going to have been made for sea trout so will be about a 7 or 8 weight and made for a river.
As for Alex Martin...an advert I saw online says "Alex Martin, Glasgow, Edinburgh and Aberdeen"...so it could be a "local" rod....which leads me back to it being a sea trout rod. They also did reels, notably The Thistle and The Caledonia.