Yes, the composition of the "conglomerate" is the key...
acid based, electrolysis, ultrasonic....
first step is to get a good xray to see what your got.
I found the best, and cheapest is to find a veterinarian that does field visits. These are the largest and most powerful xray devices (and the cheapest!) You get a big well defined image...
with this, you can start with a CO2 bath or other light acid such as oxalic to loosen it up, (limeaway used to have oxalic acid, which made it soo good)
or if from the xray, you know there is nothing there, uses an engraver/dremel to start removing pieces...this will cut down on the soak time.
Watch the acid though, muriatic will stain some metals...
I usually go to electrolysis before acid. this with an the engraver or dremel...