(1+(x-1))+(1-(x-1))=2

   1. Обозначим:

• (1 + (x - 1))^(1/3) = u;
• (1 - (x - 1))^(1/3) = v.

   Тогда:

• u^3 = 1 + (x - 1);
• v^3 = 1 - (x - 1);
• uv = (1 - x + 1)^(1/3) = (2 - x)^(1/3).

   2. Возведем уравнение в куб, воспользовавшись формулой:

• (a + b)^3 = a^3 + b^3 + 3ab(a + b);

• (1 + (x - 1))^(1/3) + (1 - (x - 1))^(1/3) = 2;

• u + v = 2;
• (u + v)^3 = 2^3;
• u^3 + v^3 + 3uv(u + v) = 8;
• 1 + (x - 1) + 1 - (x - 1) + 3 * (2 - x)^(1/3) * 2 = 8;
• 2 + 6 * (2 - x)^(1/3) = 8;
• 6 * (2 - x)^(1/3) = 6;
• (2 - x)^(1/3) = 1;
• 2 - x = 1;
• x = 2 - 1;
• x = 1.

   Ответ: 1.