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The coupled cavity Fabry-Perot additive pulse mode-locked (APM) design of an all-fiber mode-locked fiber laser is investigated theoretically. Experimental implementation of the design has already been demonstrated elsewhere, and in previous work, it was shown that contrary to a solid-state coupled cavity Fabry-Perot APM laser, an interferometric length match and stabilization of the two cavities is not needed. However, the pulse train seems to be located on top of a large CW background. In this paper, a theoretically analysis of the design based on the master equation derived by Haus is presented. Using the analytical theory developed for the master equation it is possible to determine and compare the round-trip loss for a mode-locked and for a CW solution and, hence, find the regimes where an all-fiber laser based on the design is expected to give a stable background free mode-locked output.