Agglomerated fine solids, e.g., agglomerated pellets (2B), that are located within a restricted space or pinch point of a conveyance system (1), and that impede the free-flow of fine solids from one vessel (4) to another vessel (10), are detected and fragmented through the coordinated use of a flow detector (12), breaker plate (8) and press (6). The flow detector (12) senses an interruption or diminishment in the flow of the fine solids and signals and actuates the press (6) which in turn engages and fragments the agglomeration. The breaker plate (8) is sized and configured to trap major agglomerates.