The number of distinct real roots of the equation $x ^ { 5 } \left( x ^ { 3 } - x ^ { 2 } - x + 1 \right) + x \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 4 \right) - 1 = 0$ is $\_\_\_\_$.
The number of distinct real roots of the equation $x ^ { 5 } \left( x ^ { 3 } - x ^ { 2 } - x + 1 \right) + x \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 4 \right) - 1 = 0$ is $\_\_\_\_$.