Place the cabbage in a large bowl, add 5 cups of water and 1 tablespoon of salt, and let stand for 15 to 30 minutes while you prepare the rest of the salad. (This will make the cabbage less chewy and more crisp.)
Place the pecans in a medium-size skillet over medium heat, and toast, stirring frequently (watch them closely to ensure they don’t burn), until they become fragrant and golden, 4 to 6 minutes. Add 2 teaspoons of the canola oil and a generous pinch of salt and stir to coat the nuts. Add the brown sugar and continue to stir to melt the sugar and coat the pecans, about 2 minutes. Remove from the heat and spread out the pecans on a piece of parchment paper to cool. Coarsely chop them completely.
Meanwhile, whisk together the soy sauce, vinegar, lime juice, granulated sugar, garlic, and red pepper akes in a small bowl.
Toss together the jicama, carrots, and remaining 1 tablespoon plus 1 teaspoon of oil in a large bowl. Drain the cabbage well, wrap it in a kitchen towel to absorb excess moisture, and squeeze it with your hands to encourage softening. Add the cabbage to the jicama mixture, then drizzle with the dressing to taste and toss to coat. Add about three quarters of the mint and three quarters of the grapefruit, half of the pecans, and salt, pepper, and lime juice to taste. Toss to combine.
Transfer the salad to individual plates and top with the remaining mint, grapefruit, and pecans.