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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