Is it worth replace the engine of an 11 year old fridge
Unless your refrigerator is designed to be repaired, that is a drastic repair, and it's almost certainly going to be a better choice to buy a whole new one:


Consumer fridges are designed to be assembled once, and never disassembled. There are probably plenty of pipes and wires that are glued in place and/or buried inside the structure, and are almost impossible to remove without destroying something else
You think you know what's wrong with the unit, but after you've spent a lot of money you may find that you were wrong, and haven't fixed the real problem
Even if you do manage to fix this problem, the best you'll get is an 11-year-old fridge that is may fail in some other way at any moment
Even if the fridge never fails again, it will likely be less efficient and less convenient than a new fridge. Plus, when you choose a new fridge you'll have the chance to get something that better matches your needs.