# Got dam 47

What the title is referencing

The Brilli military has established a number of dams on Pluto to collect water, since they heard that there is ice on Pluto. However, anti-Brilli forces have captured Dam Number 47 and will not release it unless it receives G dollars or the members of Brilliant.org answer this math problem.

The positive integer solutions to the equation $$x^2+47=y^3$$ can be written are $$(x_1,y_1),$$ $$(x_2,y_2),$$ and $$(x_3,y_3).$$ Find $$x_1+x_2+x_3+y_1+y_2+y_3.$$

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