Speedo cable stuck in transmission

 Newbie here.  With an MOT approaching soon, I thought I'd try and sort the odometer which has been working on an off for years. This forum has been helpful in showing how to replace the gears in the speedo housing but I thought I'd treat myself to a new speedo cable as it sometimes gets stuck at 30mph.  There is a lot of resistance when trying to pull the cable out of the transmission and I don't want to yank it until the gear might fall into the gearbox. Youtube videos seem to show the cable coming out with ease. Should I just be brave and give it a yank? Cheers.         

from memory the pressed metal 'top hat' shaped bit is wedged into the gearbox. As you point out yanking at it simply pulls the cable out leaving the plastic cog behind.

Get a razor blade or very fine screw driver under the metal and work it upwards. Once started use pointed nose pliers to pull it out along with the cable.

Not sure if a new cable will fix your problem sounds more like an issue with the clocks?

If you are trying to get the speedo gear out and it is a beatch, try this

Jack the car up to get both wheels off the ground place on jack stands.
Place the car in gear, and rotate the wheels a bit one way, then in Reverse try the other way.  

See if the gear pops out.

I have heard of this allowing the gear to work out by taking the pressure of the transmission and rotating the gear manually to allow the gear to spin a bit as you are pulling on the cable.

If the Little c-clip on the end pops off and you loose the gear internally it will usually require a rebuild, but I have heard of folks that got lucky by over filling the tranmission with oil and the gear floating up so you could grab it with a magic finger or long needle nosed pliers.  

Thanks for the tips. I haven't tried yet but will post back my successes (or failures). Clocks are probably the first option. Cheers.