The tangency point

Geometry Level 5

Let there be 2 graphs of 2 parabolas, $$(1): y = x^2$$, $$(2): x=y^2$$ as shown in the figure.

The graph of the parabola $$(1)$$ moves along the $$y$$-axis from the bottom to the top as the parabola $$(2)$$ shifts to the right.

What is the sum of coordinates of the tangency of the point?

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