\[\boxed{\text{1058\ (1058).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} \sqrt[3]{\frac{x}{y}} + \sqrt[3]{\frac{y}{x}} = 4,25 \\ x + y = 130\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[Пусть\ \ \sqrt[3]{\frac{x}{y}} = a,\ \ тогда:\]
\[a + \frac{1}{a} = 4,25,\ \ \]
\[a^{2} - 4,25a + 1 = 0\]
\[D = {4,25}^{2} - 4 = 14,0625\]
\[a_{1,2} = \frac{4,25 \pm 3,75}{2} \Longrightarrow a_{1} = 4,\]
\[a_{2} = \frac{1}{4},\]
\[1)\ \left\{ \begin{matrix} \frac{x}{y} = 64\ \ \ \ \ \ \ \ \ \ \\ x + y = 130 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 64y\ \ \ \ \\ 65y = 130 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 2\ \ \ \ \ \\ x = 128 \\ \end{matrix} \right.\ \Longrightarrow\]
\[2)\ \left\{ \begin{matrix} \frac{x}{y} = \frac{1}{64}\text{\ \ \ \ \ \ \ \ \ \ } \\ x + y = 130 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 64x\ \ \ \ \\ 65x = 130 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 2\ \ \ \ \\ y = 128 \\ \end{matrix} \right.\ \Longrightarrow\]
\[Ответ:(128;2);\ \ (2;128).\]